{"id":2033,"date":"2022-11-08T07:35:05","date_gmt":"2022-11-08T07:35:05","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=2033"},"modified":"2022-11-08T07:40:11","modified_gmt":"2022-11-08T07:40:11","slug":"ncert-solutions-class-7-maths-chapter-9-rational-numbers-ex-9-1","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-9-rational-numbers-ex-9-1\/","title":{"rendered":"NCERT Solutions Class 7 Maths Chapter 9 Rational Numbers Ex 9.1"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 7 Mathematics\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 9 (Rational Numbers)<\/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 7 Mathematics <strong>Chapter &#8211; 9 Rational Numbers <\/strong>Exercise 9.1 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Chapter : 9 Rational Numbers<\/strong><\/span><\/p>\n<ul>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-9-rational-numbers-ex-9-2\" target=\"_blank\" rel=\"noopener\"><span style=\"font-family: georgia, palatino, serif;\">NCERT Solution Class 7 Maths Exercise &#8211; 9.2<\/span><\/a><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 9.1\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>1. List five rational numbers between:<br \/>\n<\/strong><strong>(i) -1 and 0<br \/>\n(ii) -2 and -1<br \/>\n(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-4}{5}}\" alt=\"\\mathbf{\\frac{-4}{5}}\" align=\"absmiddle\" \/><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mrow\"><span id=\"MathJax-Span-5\" class=\"mo\">\u00a0<\/span><\/span><\/span><span id=\"MathJax-Span-8\" class=\"mtext\">and <\/span><span id=\"MathJax-Span-9\" class=\"mfrac\"><span id=\"MathJax-Span-10\" class=\"mrow\"><span id=\"MathJax-Span-11\" class=\"mo\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-2}{3}}\" alt=\"\\mathbf{\\frac{-2}{3}}\" align=\"absmiddle\" \/><\/span><\/span><\/span><\/span><\/span><\/span><br \/>\n(iv) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{2}}\" alt=\"\\mathbf{\\frac{1}{2}}\" align=\"absmiddle\" \/><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-14\" class=\"math\"><span id=\"MathJax-Span-15\" class=\"mrow\"><span id=\"MathJax-Span-19\" class=\"mtext\"> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{3}}\" alt=\"\\mathbf{\\frac{2}{3}}\" align=\"absmiddle\" \/><\/span><\/span><\/span><\/span><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=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(i) -1 and 0<br \/>\n<\/strong>Converting each of rational numbers as a denominator 5 + 1 = 6,<br \/>\nwe have<br \/>\n-1 = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-1\\times&amp;space;6}{6}\" alt=\"\\frac{-1\\times 6}{6}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-6}{6}\" alt=\"\\frac{-6}{6}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{0\\times&amp;space;6}{6}\" alt=\"\\frac{0\\times 6}{6}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{0}{6}\" alt=\"\\frac{0}{6}\" 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}{6}\" alt=\"\\frac{-6}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{6}\" alt=\"\\frac{-5}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4}{6}\" alt=\"\\frac{-4}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{6}\" alt=\"\\frac{-3}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-2}{6}\" alt=\"\\frac{-2}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-1}{6}\" alt=\"\\frac{-1}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{0}{6}\" alt=\"\\frac{0}{6}\" align=\"absmiddle\" \/><br \/>\n<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\">or<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">-1 &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{6}\" alt=\"\\frac{-5}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4}{6}\" alt=\"\\frac{-4}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{6}\" alt=\"\\frac{-3}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-2}{6}\" alt=\"\\frac{-2}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-1}{6}\" alt=\"\\frac{-1}{6}\" align=\"absmiddle\" \/> &lt; 0<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\">Hence,<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">the Five Rational numbers between -1 and 0 are\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{6}\" alt=\"\\frac{-5}{6}\" align=\"absmiddle\" \/> , <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4}{6}\" alt=\"\\frac{-4}{6}\" align=\"absmiddle\" \/> , <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{6}\" alt=\"\\frac{-3}{6}\" align=\"absmiddle\" \/> , <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-2}{6}\" alt=\"\\frac{-2}{6}\" align=\"absmiddle\" \/> and\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-1}{6}\" alt=\"\\frac{-1}{6}\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(ii) -2 and -1<br \/>\n<\/strong>Converting each of rational numbers as a denominator 5 + 1 = 6,<br \/>\nWe have<br \/>\n-2 = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-2\\times&amp;space;6}{6}\" alt=\"\\frac{-2\\times 6}{6}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-12}{6}\" alt=\"\\frac{-12}{6}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-1\\times&amp;space;6}{6}\" alt=\"\\frac{-1\\times 6}{6}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-6}{6}\" alt=\"\\frac{-6}{6}\" align=\"absmiddle\" \/> = -1<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-12}{6}\" alt=\"\\frac{-12}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-11}{6}\" alt=\"\\frac{-11}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-10}{6}\" alt=\"\\frac{-10}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-9}{6}\" alt=\"\\frac{-9}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-8}{6}\" alt=\"\\frac{-8}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7}{6}\" alt=\"\\frac{-7}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-6}{6}\" alt=\"\\frac{-6}{6}\" align=\"absmiddle\" \/><br \/>\n<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\">or<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">-2 &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-11}{6}\" alt=\"\\frac{-11}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-10}{6}\" alt=\"\\frac{-10}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-9}{6}\" alt=\"\\frac{-9}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-8}{6}\" alt=\"\\frac{-8}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7}{6}\" alt=\"\\frac{-7}{6}\" align=\"absmiddle\" \/> &lt; -1<br \/>\n<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\">Hence,<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">the Five Rational numbers between -2 and -1 are <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-11}{6}\" alt=\"\\frac{-11}{6}\" align=\"absmiddle\" \/> , <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-10}{6}\" alt=\"\\frac{-10}{6}\" align=\"absmiddle\" \/> , <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-9}{6}\" alt=\"\\frac{-9}{6}\" align=\"absmiddle\" \/> , <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-8}{6}\" alt=\"\\frac{-8}{6}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7}{6}\" alt=\"\\frac{-7}{6}\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-4}{5}}\" alt=\"\\mathbf{\\frac{-4}{5}}\" align=\"absmiddle\" \/><span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-4\" class=\"mrow\"><span id=\"MathJax-Span-5\" class=\"mo\">\u00a0<\/span><\/span><\/span><span id=\"MathJax-Span-8\" class=\"mtext\">and <\/span><span id=\"MathJax-Span-9\" class=\"mfrac\"><span id=\"MathJax-Span-10\" class=\"mrow\"><span id=\"MathJax-Span-11\" class=\"mo\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-2}{3}}\" alt=\"\\mathbf{\\frac{-2}{3}}\" align=\"absmiddle\" \/><br \/>\n<\/span><\/span><\/span><\/span><\/span><\/span><\/strong>Converting each of the rational numbers as a denominator (L.C.M. of 5 and 3) = 15,<br \/>\nwe have<br \/>\n<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4}{5}\" alt=\"\\frac{-4}{5}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4\\times&amp;space;3}{5\\times&amp;space;3}\" alt=\"\\frac{-4\\times 3}{5\\times 3}\" align=\"absmiddle\" \/>\u00a0= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-12}{15}\" alt=\"\\frac{-12}{15}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-2\\times&amp;space;5}{3\\times&amp;space;5}\" alt=\"\\frac{-2\\times 5}{3\\times 5}\" align=\"absmiddle\" \/>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-10}{15}\" alt=\"\\frac{-10}{15}\" align=\"absmiddle\" \/><br \/>\n<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\">Since there is only one integer i.e. -11 between -12 and -10, we have to find equivalent rational numbers.<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-12}{15}\" alt=\"\\frac{-12}{15}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-12\\times3}{15\\times&amp;space;3}\" alt=\"\\frac{-12\\times3}{15\\times 3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-36}{45}\" alt=\"\\frac{-36}{45}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-10\\times&amp;space;3}{15\\times&amp;space;3}\" alt=\"\\frac{-10\\times 3}{15\\times 3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-30}{45}\" alt=\"\\frac{-30}{45}\" 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{-36}{45}\" alt=\"\\frac{-36}{45}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-35}{45}\" alt=\"\\frac{-35}{45}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-34}{45}\" alt=\"\\frac{-34}{45}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-33}{45}\" alt=\"\\frac{-33}{45}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-32}{45}\" alt=\"\\frac{-32}{45}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-31}{45}\" alt=\"\\frac{-31}{45}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-30}{45}\" alt=\"\\frac{-30}{45}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\">or<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4}{5}\" alt=\"\\frac{-4}{5}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-35}{45}\" alt=\"\\frac{-35}{45}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-34}{45}\" alt=\"\\frac{-34}{45}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-33}{45}\" alt=\"\\frac{-33}{45}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-32}{45}\" alt=\"\\frac{-32}{45}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-31}{45}\" alt=\"\\frac{-31}{45}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-2}{3}\" alt=\"\\frac{-2}{3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\">Hence,<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">the Five Rational numbers between <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4}{5}\" alt=\"\\frac{-4}{5}\" align=\"absmiddle\" \/>\u00a0 and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-2}{3}\" alt=\"\\frac{-2}{3}\" align=\"absmiddle\" \/> are <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-35}{45}\" alt=\"\\frac{-35}{45}\" align=\"absmiddle\" \/> , <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-34}{45}\" alt=\"\\frac{-34}{45}\" align=\"absmiddle\" \/> , <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-33}{45}\" alt=\"\\frac{-33}{45}\" align=\"absmiddle\" \/> , <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-32}{45}\" alt=\"\\frac{-32}{45}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-31}{45}\" alt=\"\\frac{-31}{45}\" align=\"absmiddle\" \/> \u00a0<\/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{1}{2}}\" alt=\"\\mathbf{\\frac{1}{2}}\" align=\"absmiddle\" \/><span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-14\" class=\"math\"><span id=\"MathJax-Span-15\" class=\"mrow\"><span id=\"MathJax-Span-19\" class=\"mtext\"> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{3}}\" alt=\"\\mathbf{\\frac{2}{3}}\" align=\"absmiddle\" \/><\/span><\/span><\/span><\/span><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Converting each of the rational numbers in their equivalent rational numbers,<br \/>\nwe have<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1\\times&amp;space;3}{2\\times&amp;space;3}\" alt=\"\\frac{1\\times 3}{2\\times 3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{6}\" alt=\"\\frac{3}{6}\" align=\"absmiddle\" \/> and\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{3}\" alt=\"\\frac{2}{3}\" align=\"absmiddle\" \/> =\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2\\times&amp;space;2}{3\\times&amp;space;2}\" alt=\"\\frac{2\\times 2}{3\\times 2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{6}\" alt=\"\\frac{4}{6}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Since there is only one integer i.e. 3 between 4, we have to find equivalent rational numbers.<\/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}{6}\" alt=\"\\frac{3}{6}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3\\times&amp;space;6}{6\\times&amp;space;6}\" alt=\"\\frac{3\\times 6}{6\\times 6}\" align=\"absmiddle\" \/>\u00a0= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{18}{36}\" alt=\"\\frac{18}{36}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{6}\" alt=\"\\frac{4}{6}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4\\times&amp;space;6}{6\\times&amp;space;6}\" alt=\"\\frac{4\\times 6}{6\\times 6}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{24}{36}\" alt=\"\\frac{24}{36}\" align=\"absmiddle\" \/><br \/>\n<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2234 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{18}{36}\" alt=\"\\frac{18}{36}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{19}{36}\" alt=\"\\frac{19}{36}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{20}{36}\" alt=\"\\frac{20}{36}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{21}{36}\" alt=\"\\frac{21}{36}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{22}{36}\" alt=\"\\frac{22}{36}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{23}{36}\" alt=\"\\frac{23}{36}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{24}{36}\" alt=\"\\frac{24}{36}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\">or<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\">\u2234 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/> \u00a0&lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{19}{36}\" alt=\"\\frac{19}{36}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{9}\" alt=\"\\frac{5}{9}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{12}\" alt=\"\\frac{7}{12}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{11}{18}\" alt=\"\\frac{11}{18}\" align=\"absmiddle\" \/>\u00a0&lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{23}{36}\" alt=\"\\frac{23}{36}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{3}\" alt=\"\\frac{2}{3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\">Hence,<\/span><br \/>\n<span style=\"font-family: georgia, palatino, serif; color: #000000;\">the Five Rational numbers between <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{2}\" alt=\"\\frac{1}{2}\" align=\"absmiddle\" \/>\u00a0 and\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{3}\" alt=\"\\frac{2}{3}\" align=\"absmiddle\" \/> \u00a0are <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{19}{36}\" alt=\"\\frac{19}{36}\" align=\"absmiddle\" \/> , <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{9}\" alt=\"\\frac{5}{9}\" align=\"absmiddle\" \/> , <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{12}\" alt=\"\\frac{7}{12}\" align=\"absmiddle\" \/> , <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{11}{18}\" alt=\"\\frac{11}{18}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{23}{36}\" alt=\"\\frac{23}{36}\" align=\"absmiddle\" \/><\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>2. Write four more rational numbers in each of the following patterns:<\/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{-3}{5},&amp;space;\\frac{-6}{10},&amp;space;\\frac{-9}{15},\\frac{-12}{20},&amp;space;....}\" alt=\"\\mathbf{\\frac{-3}{5}, \\frac{-6}{10}, \\frac{-9}{15},\\frac{-12}{20}, ....}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-1}{4},&amp;space;\\frac{-2}{8},&amp;space;\\frac{-3}{12},&amp;space;...}\" alt=\"\\mathbf{\\frac{-1}{4}, \\frac{-2}{8}, \\frac{-3}{12}, ...}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-1}{6},&amp;space;\\frac{2}{-12},\\frac{3}{-18},\\frac{4}{-24}...}\" alt=\"\\mathbf{\\frac{-1}{6}, \\frac{2}{-12},\\frac{3}{-18},\\frac{4}{-24}...}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(iv) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-2}{3},\\frac{2}{-3},\\frac{4}{-6},\\frac{6}{-9},...}\" alt=\"\\mathbf{\\frac{-2}{3},\\frac{2}{-3},\\frac{4}{-6},\\frac{6}{-9},...}\" 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><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-3}{5},&amp;space;\\frac{-6}{10},&amp;space;\\frac{-9}{15},\\frac{-12}{20},&amp;space;....}\" alt=\"\\mathbf{\\frac{-3}{5}, \\frac{-6}{10}, \\frac{-9}{15},\\frac{-12}{20}, ....}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">In the above question, we can observe that the numerator and denominator are the multiples of 3 and 5.<\/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\\times&amp;space;1}{5\\times&amp;space;1},&amp;space;\\frac{-3\\times&amp;space;2}{5\\times&amp;space;2},&amp;space;\\frac{-3\\times&amp;space;3}{5\\times&amp;space;3},&amp;space;\\frac{-3\\times&amp;space;4}{5\\times&amp;space;4},...\" alt=\"\\frac{-3\\times 1}{5\\times 1}, \\frac{-3\\times 2}{5\\times 2}, \\frac{-3\\times 3}{5\\times 3}, \\frac{-3\\times 4}{5\\times 4},...\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Then, next four rational numbers in this pattern are,<\/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\\times&amp;space;5}{5\\times&amp;space;5},&amp;space;\\frac{-3\\times&amp;space;6}{5\\times&amp;space;6},&amp;space;\\frac{-3\\times&amp;space;7}{5\\times&amp;space;7},&amp;space;\\frac{-3\\times&amp;space;8}{5\\times&amp;space;8}\" alt=\"\\frac{-3\\times 5}{5\\times 5}, \\frac{-3\\times 6}{5\\times 6}, \\frac{-3\\times 7}{5\\times 7}, \\frac{-3\\times 8}{5\\times 8}\" 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}{25},&amp;space;\\frac{-18}{30},\\frac{-21}{35},&amp;space;\\frac{-24}{40}\" alt=\"\\frac{-15}{25}, \\frac{-18}{30},\\frac{-21}{35}, \\frac{-24}{40}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif; color: #000000;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-1}{4},&amp;space;\\frac{-2}{8},&amp;space;\\frac{-3}{12},&amp;space;...}\" alt=\"\\mathbf{\\frac{-1}{4}, \\frac{-2}{8}, \\frac{-3}{12}, ...}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">In the above question, we can observe that the numerator and denominator are the multiples of 1 and 4.<\/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\\times&amp;space;1}{4\\times&amp;space;1},&amp;space;\\frac{-1\\times&amp;space;2}{4\\times&amp;space;2},&amp;space;\\frac{-1\\times&amp;space;3}{4\\times&amp;space;3},&amp;space;...\" alt=\"\\frac{-1\\times 1}{4\\times 1}, \\frac{-1\\times 2}{4\\times 2}, \\frac{-1\\times 3}{4\\times 3}, ...\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Then, next four rational numbers in this pattern are,<\/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\\times4}{4\\times&amp;space;4},&amp;space;\\frac{-1\\times&amp;space;5}{4\\times&amp;space;5},&amp;space;\\frac{-1\\times&amp;space;6}{4\\times&amp;space;6},&amp;space;\\frac{-1\\times&amp;space;7}{4\\times&amp;space;7}\" alt=\"\\frac{-1\\times4}{4\\times 4}, \\frac{-1\\times 5}{4\\times 5}, \\frac{-1\\times 6}{4\\times 6}, \\frac{-1\\times 7}{4\\times 7}\" 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}{16},\\frac{-5}{20},\\frac{-6}{24},\\frac{-7}{28}\" alt=\"\\frac{-4}{16},\\frac{-5}{20},\\frac{-6}{24},\\frac{-7}{28}\" align=\"absmiddle\" \/><\/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}{6},&amp;space;\\frac{2}{-12},\\frac{3}{-18},\\frac{4}{-24}...}\" alt=\"\\mathbf{\\frac{-1}{6}, \\frac{2}{-12},\\frac{3}{-18},\\frac{4}{-24}...}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">In the above question, we can observe that the numerator and denominator are the multiples of 1 and 6.<\/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\\times&amp;space;1}{6\\times&amp;space;1},\\frac{1\\times&amp;space;2}{6\\times&amp;space;-2},&amp;space;\\frac{-1\\times&amp;space;3}{6\\times&amp;space;-3},&amp;space;\\frac{-1\\times&amp;space;4}{6\\times&amp;space;-4}\" alt=\"\\frac{-1\\times 1}{6\\times 1},\\frac{1\\times 2}{6\\times -2}, \\frac{-1\\times 3}{6\\times -3}, \\frac{-1\\times 4}{6\\times -4}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Then, next four rational numbers in this pattern are,<\/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\\times&amp;space;5}{6\\times&amp;space;5},\\frac{1\\times&amp;space;6}{6\\times&amp;space;-6},&amp;space;\\frac{-1\\times&amp;space;7}{6\\times&amp;space;-7},&amp;space;\\frac{-1\\times&amp;space;8}{6\\times&amp;space;-8}\" alt=\"\\frac{-1\\times 5}{6\\times 5},\\frac{1\\times 6}{6\\times -6}, \\frac{-1\\times 7}{6\\times -7}, \\frac{-1\\times 8}{6\\times -8}\" 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{-5}{30},\\frac{6}{-36},\\frac{7}{-42},\\frac{8}{-48}\" alt=\"\\frac{-5}{30},\\frac{6}{-36},\\frac{7}{-42},\\frac{8}{-48}\" align=\"absmiddle\" \/><\/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{-2}{3},\\frac{2}{-3},\\frac{4}{-6},\\frac{6}{-9},...}\" alt=\"\\mathbf{\\frac{-2}{3},\\frac{2}{-3},\\frac{4}{-6},\\frac{6}{-9},...}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">In the above question, we can observe that the numerator and denominator are the multiples of 2 and 3.<\/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\\times&amp;space;1}{3\\times&amp;space;1},\\frac{2\\times&amp;space;1}{-3\\times&amp;space;1},&amp;space;\\frac{2\\times&amp;space;2}{-3\\times&amp;space;2},\\frac{2\\times&amp;space;3}{-3\\times&amp;space;3}...\" alt=\"\\frac{-2\\times 1}{3\\times 1},\\frac{2\\times 1}{-3\\times 1}, \\frac{2\\times 2}{-3\\times 2},\\frac{2\\times 3}{-3\\times 3}...\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Then, next four rational numbers in this pattern are,<\/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\\times&amp;space;4}{-3\\times&amp;space;4},\\frac{2\\times&amp;space;5}{-3\\times&amp;space;5},&amp;space;\\frac{2\\times&amp;space;6}{-3\\times&amp;space;6},\\frac{2\\times&amp;space;7}{-3\\times&amp;space;7},\" alt=\"\\frac{2\\times 4}{-3\\times 4},\\frac{2\\times 5}{-3\\times 5}, \\frac{2\\times 6}{-3\\times 6},\\frac{2\\times 7}{-3\\times 7},\" 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{8}{-12},\\frac{10}{-15},\\frac{12}{-18},\\frac{14}{-21}\" alt=\"\\frac{8}{-12},\\frac{10}{-15},\\frac{12}{-18},\\frac{14}{-21}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>3. Give four rational numbers equivalent to:<\/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?\\boldsymbol{\\frac{-2}{7}}\" alt=\"\\boldsymbol{\\frac{-2}{7}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/strong><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{5}{-3}}\" alt=\"\\mathbf{\\frac{5}{-3}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/strong><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{4}{9}}\" alt=\"\\mathbf{\\frac{4}{9}}\" 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?\\boldsymbol{\\frac{-2}{7}}\" alt=\"\\boldsymbol{\\frac{-2}{7}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The four rational numbers equivalent to <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-2}{7}\" alt=\"\\frac{-2}{7}\" align=\"absmiddle\" \/> are,<\/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\\times&amp;space;2}{7\\times&amp;space;2},\\frac{-2\\times&amp;space;3}{7\\times&amp;space;3},&amp;space;\\frac{-2\\times&amp;space;4}{7\\times&amp;space;4},&amp;space;\\frac{-2\\times&amp;space;5}{7\\times&amp;space;5}\" alt=\"\\frac{-2\\times 2}{7\\times 2},\\frac{-2\\times 3}{7\\times 3}, \\frac{-2\\times 4}{7\\times 4}, \\frac{-2\\times 5}{7\\times 5}\" 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}{14},\\frac{-6}{21},\\frac{-8}{28},\\frac{-10}{35}\" alt=\"\\frac{-4}{14},\\frac{-6}{21},\\frac{-8}{28},\\frac{-10}{35}\" align=\"absmiddle\" \/><\/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{5}{-3}}\" alt=\"\\mathbf{\\frac{5}{-3}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The four rational numbers equivalent to <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{-3}\" alt=\"\\frac{5}{-3}\" align=\"absmiddle\" \/> are,<\/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{5\\times&amp;space;2}{-3\\times&amp;space;2},\\frac{5\\times&amp;space;3}{-3\\times&amp;space;3},&amp;space;\\frac{5\\times&amp;space;4}{-3\\times&amp;space;4},\\frac{5\\times&amp;space;5}{-3\\times&amp;space;5}\" alt=\"\\frac{5\\times 2}{-3\\times 2},\\frac{5\\times 3}{-3\\times 3}, \\frac{5\\times 4}{-3\\times 4},\\frac{5\\times 5}{-3\\times 5}\" 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}{-6},\\frac{15}{-9},\\frac{20}{-12},\\frac{25}{-15}\" alt=\"\\frac{10}{-6},\\frac{15}{-9},\\frac{20}{-12},\\frac{25}{-15}\" align=\"absmiddle\" \/><\/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{4}{9}}\" alt=\"\\mathbf{\\frac{4}{9}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The four rational numbers equivalent to <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{9}\" alt=\"\\frac{4}{9}\" align=\"absmiddle\" \/> are,<\/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\\times&amp;space;2}{9\\times&amp;space;2},\\frac{4\\times&amp;space;3}{9\\times&amp;space;3},&amp;space;\\frac{4\\times&amp;space;4}{9\\times&amp;space;4},\\frac{4\\times&amp;space;5}{9\\times&amp;space;5}\" alt=\"\\frac{4\\times 2}{9\\times 2},\\frac{4\\times 3}{9\\times 3}, \\frac{4\\times 4}{9\\times 4},\\frac{4\\times 5}{9\\times 5}\" 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{8}{18},\\frac{12}{27},\\frac{16}{36},\\frac{20}{45}\" alt=\"\\frac{8}{18},\\frac{12}{27},\\frac{16}{36},\\frac{20}{45}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>4. Draw the number line and represent the following rational numbers on it:<\/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{3}{4}}\" alt=\"\\mathbf{\\frac{3}{4}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-5}{8}}\" alt=\"\\mathbf{\\frac{-5}{8}}\" 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{-7}{4}}\" alt=\"\\mathbf{\\frac{-7}{4}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (iv) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{7}{8}}\" alt=\"\\mathbf{\\frac{7}{8}}\" 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><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{3}{4}}\" alt=\"\\mathbf{\\frac{3}{4}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">We know that <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{4}\" alt=\"\\frac{3}{4}\" align=\"absmiddle\" \/>\u00a0 is greater than 0 and less than 1.<br \/>\n\u2234 it lies between 0 and 1. It can be represented on number line as,<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2041 \" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q4-a.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"416\" height=\"67\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q4-a.png 329w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q4-a-300x48.png 300w\" sizes=\"auto, (max-width: 416px) 100vw, 416px\" \/><br \/>\n<\/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{-5}{8}}\" alt=\"\\mathbf{\\frac{-5}{8}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">We know that <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{8}\" alt=\"\\frac{-5}{8}\" align=\"absmiddle\" \/> is less than 0 and greater than -1.<br \/>\n\u2234 it lies between 0 and -1. It can be represented on number line as,<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2042\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q4-b.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"461\" height=\"87\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q4-b.png 334w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q4-b-300x57.png 300w\" sizes=\"auto, (max-width: 461px) 100vw, 461px\" \/><\/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{-7}{4}}\" alt=\"\\mathbf{\\frac{-7}{4}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Now above question can be written as, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7}{4}\" alt=\"\\frac{-7}{4}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-1\\frac{3}{4}\" alt=\"-1\\frac{3}{4}\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">We know that <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7}{4}\" alt=\"\\frac{-7}{4}\" align=\"absmiddle\" \/> is Less than -1 and greater than -2.<br \/>\n\u2234 it lies between -1 and -2. It can be represented on number line as,<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2043\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q4-c.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"467\" height=\"70\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q4-c.png 367w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q4-c-300x45.png 300w\" sizes=\"auto, (max-width: 467px) 100vw, 467px\" \/><\/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{7}{8}}\" alt=\"\\mathbf{\\frac{7}{8}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">We know that 7\/8 is greater than 0 and less than 1.<br \/>\n\u2234 it lies between 0 and 1. It can be represented on number line as,<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2044\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q4-d.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"441\" height=\"69\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q4-d.png 371w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q4-d-300x47.png 300w\" sizes=\"auto, (max-width: 441px) 100vw, 441px\" \/><br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>5. The points P, Q, R, S, T, U, A and B on the number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R and S.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-2045\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q5.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"743\" height=\"67\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q5.png 821w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q5-300x27.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q5-768x69.png 768w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-9.1-Q5-480x43.png 480w\" sizes=\"auto, (max-width: 743px) 100vw, 743px\" \/><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<br \/>\n<\/strong>The distance between A and B = 1 unit<br \/>\nAnd it is divided into 3 equal parts = AP = PQ = QB = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{3}\" alt=\"\\frac{1}{3}\" align=\"absmiddle\" \/><br \/>\nP = 2 + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{3}\" alt=\"\\frac{1}{3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(6+1)}{3}\" alt=\"\\frac{(6+1)}{3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{3}\" alt=\"\\frac{7}{3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Q = 2 + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{3}\" alt=\"\\frac{2}{3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(6+2)}{3}\" alt=\"\\frac{(6+2)}{3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8}{3}\" alt=\"\\frac{8}{3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Similarly,<br \/>\nThe distance between U and T = 1 unit<br \/>\nAnd it is divided into 3 equal parts = TR = RS = SU = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{3}\" alt=\"\\frac{1}{3}\" align=\"absmiddle\" \/><br \/>\nR = \u2013 1 \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{3}\" alt=\"\\frac{1}{3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(-3-1)}{3}\" alt=\"\\frac{(-3-1)}{3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4}{3}\" alt=\"\\frac{-4}{3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">S = \u2013 1 \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{3}\" alt=\"\\frac{2}{3}\" align=\"absmiddle\" \/> \u00a0= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{(-3-2)}{3}\" alt=\"\\frac{(-3-2)}{3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{3}\" alt=\"\\frac{-5}{3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>6. Which of the following pairs represent the same rational number?<\/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{-7}{21}}\" alt=\"\\mathbf{\\frac{-7}{21}}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{3}{9}}\" alt=\"\\mathbf{\\frac{3}{9}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-16}{20}}\" alt=\"\\mathbf{\\frac{-16}{20}}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{20}{-25}}\" alt=\"\\mathbf{\\frac{20}{-25}}\" 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{-2}{-3}}\" alt=\"\\mathbf{\\frac{-2}{-3}}\" align=\"absmiddle\" \/>\u00a0 and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{3}}\" alt=\"\\mathbf{\\frac{2}{3}}\" 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{-3}{5}}\" alt=\"\\mathbf{\\frac{-3}{5}}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-12}{20}}\" alt=\"\\mathbf{\\frac{-12}{20}}\" 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{-7}{21}}\" alt=\"\\mathbf{\\frac{-7}{21}}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{3}{9}}\" alt=\"\\mathbf{\\frac{3}{9}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">LCM of 21 and 9 = 189<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7\\times&amp;space;9}{21\\times&amp;space;9}\" alt=\"\\frac{-7\\times 9}{21\\times 9}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3\\times&amp;space;21}{9\\times&amp;space;21}\" alt=\"\\frac{3\\times 21}{9\\times 21}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-63}{189}\" alt=\"\\frac{-63}{189}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{63}{189}\" alt=\"\\frac{63}{189}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Since &#8211; 63 \u2260 63, <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So,\u00a0\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7}{21}\" alt=\"\\frac{-7}{21}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{9}\" alt=\"\\frac{3}{9}\" align=\"absmiddle\" \/>\u00a0 pair is not represents the same rational number<strong>.<\/strong><\/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{-16}{20}}\" alt=\"\\mathbf{\\frac{-16}{20}}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{20}{-25}}\" alt=\"\\mathbf{\\frac{20}{-25}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">LCM of 20 and 25 = 100<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-16\\times&amp;space;5}{20\\times&amp;space;5}\" alt=\"\\frac{-16\\times 5}{20\\times 5}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{20\\times&amp;space;4}{-25\\times&amp;space;4}\" alt=\"\\frac{20\\times 4}{-25\\times 4}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-80}{100}\" alt=\"\\frac{-80}{100}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{80}{-100}\" alt=\"\\frac{80}{-100}\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{80}{100}\" alt=\"-\\frac{80}{100}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{80}{100}\" alt=\"-\\frac{80}{100}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Since &#8211; 80 = 80, <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So,\u00a0\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-16}{20}\" alt=\"\\frac{-16}{20}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{20}{-25}\" alt=\"\\frac{20}{-25}\" align=\"absmiddle\" \/>\u00a0 pair is represents the same rational number<strong>.<\/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{-2}{-3}}\" alt=\"\\mathbf{\\frac{-2}{-3}}\" align=\"absmiddle\" \/>\u00a0 and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{3}}\" alt=\"\\mathbf{\\frac{2}{3}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here, we have the same numerator and denominator. So <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-2}{-3}\" alt=\"\\frac{-2}{-3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{3}\" alt=\"\\frac{2}{3}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{3}\" alt=\"\\frac{2}{3}\" align=\"absmiddle\" \/> represents the same rational number<strong>.<\/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{-3}{5}}\" alt=\"\\mathbf{\\frac{-3}{5}}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-12}{20}}\" alt=\"\\mathbf{\\frac{-12}{20}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">LCM of 5 and 20 = 20<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3\\times&amp;space;4}{5\\times&amp;space;4}\" alt=\"\\frac{-3\\times 4}{5\\times 4}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-12}{20}\" alt=\"\\frac{-12}{20}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-12}{20}\" alt=\"\\frac{-12}{20}\" align=\"absmiddle\" \/>\u00a0and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-12}{20}\" alt=\"\\frac{-12}{20}\" align=\"absmiddle\" \/> \u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Since &#8211; 12 = &#8211; 12, <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So,\u00a0\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{5}\" alt=\"\\frac{-3}{5}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-12}{20}\" alt=\"\\frac{-12}{20}\" align=\"absmiddle\" \/> pair is represents the same rational number<strong>.<\/strong><\/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{8}{-5}}\" alt=\"\\mathbf{\\frac{8}{-5}}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-24}{15}}\" alt=\"\\mathbf{\\frac{-24}{15}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">LCM of 5 and 15 = 15<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8\\times&amp;space;3}{-5\\times&amp;space;3}\" alt=\"\\frac{8\\times 3}{-5\\times 3}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-24}{15}\" alt=\"\\frac{-24}{15}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{24}{-15}\" alt=\"\\frac{24}{-15}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-24}{15}\" alt=\"\\frac{-24}{15}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{24}{15}\" alt=\"-\\frac{24}{15}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{24}{15}\" alt=\"-\\frac{24}{15}\" align=\"absmiddle\" \/> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Since 24 = 24, <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8}{-5}\" alt=\"\\frac{8}{-5}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-24}{15}\" alt=\"\\frac{-24}{15}\" align=\"absmiddle\" \/>\u00a0pair is represents the same rational number<strong>.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(vi) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{3}}\" alt=\"\\mathbf{\\frac{1}{3}}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-1}{9}}\" alt=\"\\mathbf{\\frac{-1}{9}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">LCM of 3 and 9 = 9<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1\\times&amp;space;3}{3\\times&amp;space;3}\" alt=\"\\frac{1\\times 3}{3\\times 3}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-1}{9}\" alt=\"\\frac{-1}{9}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{9}\" alt=\"\\frac{3}{9}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-1}{9}\" alt=\"\\frac{-1}{9}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Since 3 \u2260 -1, <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{3}\" alt=\"\\frac{1}{3}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-1}{9}\" alt=\"\\frac{-1}{9}\" align=\"absmiddle\" \/> pair is not represents the same rational number<strong>.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(vii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-5}{-9}}\" alt=\"\\mathbf{\\frac{-5}{-9}}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{5}{-9}}\" alt=\"\\mathbf{\\frac{5}{-9}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{-9}\" alt=\"\\frac{-5}{-9}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{9}\" alt=\"\\frac{5}{9}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{-9}\" alt=\"\\frac{5}{-9}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Since 5 \u2260 -5, <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{-9}\" alt=\"\\frac{-5}{-9}\" align=\"absmiddle\" \/> and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{-9}\" alt=\"\\frac{5}{-9}\" align=\"absmiddle\" \/>\u00a0pair is not represents the same rational number<strong>.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>7. Rewrite the following rational numbers in the simplest form:<\/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{-8}{6}}\" alt=\"\\mathbf{\\frac{-8}{6}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{25}{45}}\" alt=\"\\mathbf{\\frac{25}{45}}\" 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{-8}{6}}\" alt=\"\\mathbf{\\frac{-8}{6}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-8\\div2}{6\\div2}\" alt=\"\\frac{-8\\div2}{6\\div2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4}{3}\" alt=\"\\frac{-4}{3}\" align=\"absmiddle\" \/>\u00a0 [<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\because\" alt=\"\\because\" align=\"absmiddle\" \/> HCF of 8 and 6 = 2]<\/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{25}{45}}\" alt=\"\\mathbf{\\frac{25}{45}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{25\\div5}{45\\div5}\" alt=\"\\frac{25\\div5}{45\\div5}\" align=\"absmiddle\" \/> = <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?\\because\" alt=\"\\because\" align=\"absmiddle\" \/> HCF of 25 and 45 = 5]<\/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{-44}{72}}\" alt=\"\\mathbf{\\frac{-44}{72}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-44\\div4}{72\\div4}\" alt=\"\\frac{-44\\div4}{72\\div4}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-11}{18}\" alt=\"\\frac{-11}{18}\" align=\"absmiddle\" \/>\u00a0 [<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\because\" alt=\"\\because\" align=\"absmiddle\" \/> HCF of 44 and 72 = 4]<\/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{-8}{10}}\" alt=\"\\mathbf{\\frac{-8}{10}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-8\\div2}{10\\div2}\" alt=\"\\frac{-8\\div2}{10\\div2}\" align=\"absmiddle\" \/> \u00a0= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4}{5}\" alt=\"\\frac{-4}{5}\" align=\"absmiddle\" \/>\u00a0 [<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\because\" alt=\"\\because\" align=\"absmiddle\" \/> HCF of 8 and 10 = 2]<\/span><\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>8. Fill in the boxes with the correct symbol out of &gt;, &lt;, and =.<\/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{-5}{7}}\" alt=\"\\mathbf{\\frac{-5}{7}}\" align=\"absmiddle\" \/> [ ] <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{3}}\" alt=\"\\mathbf{\\frac{2}{3}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-4}{5}}\" alt=\"\\mathbf{\\frac{-4}{5}}\" align=\"absmiddle\" \/> [ ] <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-5}{7}}\" alt=\"\\mathbf{\\frac{-5}{7}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (iii)\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-7}{8}}\" alt=\"\\mathbf{\\frac{-7}{8}}\" align=\"absmiddle\" \/> [ ] <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{14}{-16}}\" alt=\"\\mathbf{\\frac{14}{-16}}\" 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{-8}{5}}\" alt=\"\\mathbf{\\frac{-8}{5}}\" align=\"absmiddle\" \/> [ ] <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-7}{4}}\" alt=\"\\mathbf{\\frac{-7}{4}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(v) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{-3}}\" alt=\"\\mathbf{\\frac{1}{-3}}\" align=\"absmiddle\" \/> [ ] <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-1}{4}}\" alt=\"\\mathbf{\\frac{-1}{4}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(vi) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{5}{-11}}\" alt=\"\\mathbf{\\frac{5}{-11}}\" align=\"absmiddle\" \/> [ ] <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-5}{11}}\" alt=\"\\mathbf{\\frac{-5}{11}}\" align=\"absmiddle\" \/> <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(vii) 0 [ ] <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-7}{6}}\" alt=\"\\mathbf{\\frac{-7}{6}}\" 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><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\"><strong>(i) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-5}{7}}\" alt=\"\\mathbf{\\frac{-5}{7}}\" align=\"absmiddle\" \/> [ ] <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{3}}\" alt=\"\\mathbf{\\frac{2}{3}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"color: #000000;\">The LCM of the denominators 7 and 3 is 21<br \/>\n<\/span><span style=\"color: #000000;\">\u2234 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{7}\" alt=\"\\frac{-5}{7}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5&amp;space;\\times&amp;space;3}{7&amp;space;\\times&amp;space;3}\" alt=\"\\frac{-5 \\times 3}{7 \\times 3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-15}{21}\" alt=\"\\frac{-15}{21}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">and <\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif; text-align: justify;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{3}\" alt=\"\\frac{2}{3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2&amp;space;\\times&amp;space;7}{3&amp;space;\\times&amp;space;7}\" alt=\"\\frac{2 \\times 7}{3 \\times 7}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{14}{21}\" alt=\"\\frac{14}{21}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">Now, <\/span><span style=\"color: #000000;\">-15 &lt; 14<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-15}{21}\" alt=\"\\frac{-15}{21}\" align=\"absmiddle\" \/> &lt; <span style=\"color: #000000; text-align: justify;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{14}{21}\" alt=\"\\frac{14}{21}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Hence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{7}\" alt=\"\\frac{-5}{7}\" align=\"absmiddle\" \/> <strong>[&lt;]<\/strong> <span style=\"color: #000000; text-align: justify;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{3}\" alt=\"\\frac{2}{3}\" align=\"absmiddle\" \/><\/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{-4}{5}}\" alt=\"\\mathbf{\\frac{-4}{5}}\" align=\"absmiddle\" \/> [ ] <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-5}{7}}\" alt=\"\\mathbf{\\frac{-5}{7}}\" align=\"absmiddle\" \/> <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The LCM of the denominators 5 and 7 is 35<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4}{5}\" alt=\"\\frac{-4}{5}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4\\times&amp;space;7}{5\\times&amp;space;7}\" alt=\"\\frac{-4\\times 7}{5\\times 7}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-28}{35}\" alt=\"\\frac{-28}{35}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">and <\/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{-5}{7}\" alt=\"\\frac{-5}{7}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5\\times&amp;space;5}{7\\times&amp;space;5}\" alt=\"\\frac{-5\\times 5}{7\\times 5}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-25}{35}\" alt=\"\\frac{-25}{35}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">Now, <\/span><span style=\"color: #000000;\">-28 &lt; -25<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-28}{35}\" alt=\"\\frac{-28}{35}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-25}{35}\" alt=\"\\frac{-25}{35}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Hence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4}{5}\" alt=\"\\frac{-4}{5}\" align=\"absmiddle\" \/><strong> [&lt;]<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{7}\" alt=\"\\frac{-5}{7}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii)\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-7}{8}}\" alt=\"\\mathbf{\\frac{-7}{8}}\" align=\"absmiddle\" \/> [ ] <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{14}{-16}}\" alt=\"\\mathbf{\\frac{14}{-16}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{14}{-16}\" alt=\"\\frac{14}{-16}\" align=\"absmiddle\" \/> can be simplified further,<br \/>\n<\/span><span style=\"color: #000000;\">Then,<br \/>\n<\/span><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{-8}\" alt=\"\\frac{7}{-8}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8212;&#8212;- [\u2235 Divide both numerator and denominator by 2]<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7}{8}\" alt=\"\\frac{-7}{8}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{-8}\" alt=\"\\frac{7}{-8}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Hence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7}{8}\" alt=\"\\frac{-7}{8}\" align=\"absmiddle\" \/> <strong>[=]<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{14}{-16}\" alt=\"\\frac{14}{-16}\" align=\"absmiddle\" \/><\/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{-8}{5}}\" alt=\"\\mathbf{\\frac{-8}{5}}\" align=\"absmiddle\" \/> [ ] <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-7}{4}}\" alt=\"\\mathbf{\\frac{-7}{4}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 <\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The LCM of the denominators 5 and 4 is 20<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-8}{5}\" alt=\"\\frac{-8}{5}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-8\\times&amp;space;4}{5\\times&amp;space;4}\" alt=\"\\frac{-8\\times 4}{5\\times 4}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-32}{20}\" alt=\"\\frac{-32}{20}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">and <\/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{-7}{4}\" alt=\"\\frac{-7}{4}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7\\times&amp;space;5}{4\\times&amp;space;5}\" alt=\"\\frac{-7\\times 5}{4\\times 5}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-35}{20}\" alt=\"\\frac{-35}{20}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">Now,\u00a0 \u2013 <\/span><span style=\"color: #000000;\">32 &gt; \u2013 35<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-32}{20}\" alt=\"\\frac{-32}{20}\" align=\"absmiddle\" \/> &gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-35}{20}\" alt=\"\\frac{-35}{20}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Hence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-8}{5}\" alt=\"\\frac{-8}{5}\" align=\"absmiddle\" \/>\u00a0<strong>[&gt;]<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7}{4}\" alt=\"\\frac{-7}{4}\" align=\"absmiddle\" \/><\/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{1}{-3}}\" alt=\"\\mathbf{\\frac{1}{-3}}\" align=\"absmiddle\" \/> [ ] <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-1}{4}}\" alt=\"\\mathbf{\\frac{-1}{4}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">The LCM of the denominators 3 and 4 is 12<br \/>\n<\/span><span style=\"color: #000000;\">\u2234 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{-3}\" alt=\"\\frac{1}{-3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1\\times&amp;space;4}{-3\\times&amp;space;4}\" alt=\"\\frac{1\\times 4}{-3\\times 4}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{-12}\" alt=\"\\frac{4}{-12}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">and <\/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}{4}\" alt=\"\\frac{-1}{4}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-1\\times&amp;space;3}{4\\times&amp;space;3}\" alt=\"\\frac{-1\\times 3}{4\\times 3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{12}\" alt=\"\\frac{-3}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">Now, \u2013 <\/span><span style=\"color: #000000;\">4 &lt; \u2013 3<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{-12}\" alt=\"\\frac{4}{-12}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{12}\" alt=\"\\frac{-3}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Hence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{-3}\" alt=\"\\frac{1}{-3}\" align=\"absmiddle\" \/> <strong>[&lt;]<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-1}{4}\" alt=\"\\frac{-1}{4}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(vi) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{5}{-11}}\" alt=\"\\mathbf{\\frac{5}{-11}}\" align=\"absmiddle\" \/> [ ] <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-5}{11}}\" alt=\"\\mathbf{\\frac{-5}{11}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Since, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{-11}\" alt=\"\\frac{5}{-11}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{11}\" alt=\"\\frac{-5}{11}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Hence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{-11}\" alt=\"\\frac{5}{-11}\" align=\"absmiddle\" \/> <strong>[=]<\/strong> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{11}\" alt=\"\\frac{-5}{11}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(vii) 0 [ ] <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-7}{6}}\" alt=\"\\mathbf{\\frac{-7}{6}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">Since every negative rational number is less than 0.<br \/>\n<\/span><span style=\"color: #000000;\">We have\u00a0 <\/span><span style=\"color: #000000;\">0 <strong>[&gt;] <\/strong><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7}{6}\" alt=\"\\frac{-7}{6}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>9. Which is greater in each of the following:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\"><strong>(i) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{3}}\" alt=\"\\mathbf{\\frac{2}{3}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{5}{2}}\" alt=\"\\mathbf{\\frac{5}{2}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/strong><\/span><span style=\"color: #000000;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-5}{6}}\" alt=\"\\mathbf{\\frac{-5}{6}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-4}{3}}\" alt=\"\\mathbf{\\frac{-4}{3}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/strong><\/span><span style=\"color: #000000;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-3}{4}}\" alt=\"\\mathbf{\\frac{-3}{4}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{-3}}\" alt=\"\\mathbf{\\frac{2}{-3}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/strong> <\/span><\/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{-1}{4}}\" alt=\"\\mathbf{\\frac{-1}{4}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{4}}\" alt=\"\\mathbf{\\frac{1}{4}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (v) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{-3\\frac{2}{7}}\" alt=\"\\mathbf{-3\\frac{2}{7}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{-3\\frac{4}{5}}\" alt=\"\\mathbf{-3\\frac{4}{5}}\" 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=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\"><strong>(i) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{3}}\" alt=\"\\mathbf{\\frac{2}{3}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{5}{2}}\" alt=\"\\mathbf{\\frac{5}{2}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"color: #000000;\">The LCM of the denominators 3 and 2 is 6<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2\\times&amp;space;2}{3\\times&amp;space;2}\" alt=\"\\frac{2\\times 2}{3\\times 2}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5\\times&amp;space;3}{2\\times&amp;space;3}\" alt=\"\\frac{5\\times 3}{2\\times 3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{6}\" alt=\"\\frac{4}{6}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{6}\" alt=\"\\frac{15}{6}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 4 &lt; 15<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{6}\" alt=\"\\frac{4}{6}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{6}\" alt=\"\\frac{15}{6}\" align=\"absmiddle\" \/> <\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">\u2234 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{3}\" alt=\"\\frac{2}{3}\" align=\"absmiddle\" \/> &lt; <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; font-family: georgia, palatino, serif;\">Hence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{2}\" alt=\"\\frac{5}{2}\" align=\"absmiddle\" \/> is greater.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-5}{6}}\" alt=\"\\mathbf{\\frac{-5}{6}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-4}{3}}\" alt=\"\\mathbf{\\frac{-4}{3}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"color: #000000;\">The LCM of the denominators 6 and 3 is 6<\/span><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{6}\" alt=\"\\frac{-5}{6}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4\\times&amp;space;2}{3\\times&amp;space;2}\" alt=\"\\frac{-4\\times 2}{3\\times 2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{6}\" alt=\"\\frac{-5}{6}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-8}{6}\" alt=\"\\frac{-8}{6}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">\u21d2 <\/span><span style=\"color: #000000;\">-5 &gt; -8<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{6}\" alt=\"\\frac{-5}{6}\" align=\"absmiddle\" \/> &gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-8}{6}\" alt=\"\\frac{-8}{6}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{6}\" alt=\"\\frac{-5}{6}\" align=\"absmiddle\" \/>&gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4}{3}\" alt=\"\\frac{-4}{3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Hence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{6}\" alt=\"\\frac{-5}{6}\" align=\"absmiddle\" \/> is greater.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-3}{4}}\" alt=\"\\mathbf{\\frac{-3}{4}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{-3}}\" alt=\"\\mathbf{\\frac{2}{-3}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"color: #000000;\">The LCM of the denominators 4 and 3 is 12<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3\\times&amp;space;3}{4\\times&amp;space;3}\" alt=\"\\frac{-3\\times 3}{4\\times 3}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2\\times&amp;space;4}{-3\\times&amp;space;4}\" alt=\"\\frac{2\\times 4}{-3\\times 4}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-9}{12}\" alt=\"\\frac{-9}{12}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8}{-12}\" alt=\"\\frac{8}{-12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">\u21d2\u00a0<\/span><span style=\"color: #000000;\">-9 &lt; -8<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-9}{12}\" alt=\"\\frac{-9}{12}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8}{-12}\" alt=\"\\frac{8}{-12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{4}\" alt=\"\\frac{-3}{4}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{-3}\" alt=\"\\frac{2}{-3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Hence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{-3}\" alt=\"\\frac{2}{-3}\" align=\"absmiddle\" \/> is greater.<\/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{-1}{4}}\" alt=\"\\mathbf{\\frac{-1}{4}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{4}}\" alt=\"\\mathbf{\\frac{1}{4}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 Each Positive number is greater than its negative\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-1}{4}\" alt=\"\\frac{-1}{4}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{4}\" alt=\"\\frac{1}{4}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Hence <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{4}\" alt=\"\\frac{1}{4}\" align=\"absmiddle\" \/> is greater<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><strong><span style=\"color: #000000;\">(v) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{-3\\frac{2}{7}}\" alt=\"\\mathbf{-3\\frac{2}{7}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{-3\\frac{4}{5}}\" alt=\"\\mathbf{-3\\frac{4}{5}}\" align=\"absmiddle\" \/><\/span><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{23}{7}\" alt=\"-\\frac{23}{7}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{19}{5}\" alt=\"-\\frac{19}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The LCM of the denominators 7 and 5 is 35<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-23\\times&amp;space;5}{7\\times&amp;space;5}\" alt=\"\\frac{-23\\times 5}{7\\times 5}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-19\\times&amp;space;7}{5\\times&amp;space;7}\" alt=\"\\frac{-19\\times 7}{5\\times 7}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-115}{35}\" alt=\"\\frac{-115}{35}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-133}{35}\" alt=\"\\frac{-133}{35}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">Now, <\/span><span style=\"color: #000000;\">-115 &gt; -133<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">So, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-115}{35}\" alt=\"\\frac{-115}{35}\" align=\"absmiddle\" \/> &gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-133}{35}\" alt=\"\\frac{-133}{35}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-3\\frac{2}{7}\" alt=\"-3\\frac{2}{7}\" align=\"absmiddle\" \/> &gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-3\\frac{4}{5}\" alt=\"-3\\frac{4}{5}\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">Hence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-3\\frac{2}{7}\" alt=\"-3\\frac{2}{7}\" align=\"absmiddle\" \/> <\/span><span style=\"color: #000000;\">is greater.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>10. Write the following rational numbers in ascending order:<\/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{-3}{5}}\" alt=\"\\mathbf{\\frac{-3}{5}}\" align=\"absmiddle\" \/>, <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{-1}{5}}\" alt=\"\\mathbf{\\frac{-1}{5}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/strong><\/span><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-1}{3}}\" alt=\"\\mathbf{\\frac{-1}{3}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-2}{9}}\" alt=\"\\mathbf{\\frac{-2}{9}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-4}{3}}\" alt=\"\\mathbf{\\frac{-4}{3}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <\/strong><\/span><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii) <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{-3}{2}}\" alt=\"\\mathbf{\\frac{-3}{2}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-3}{4}}\" alt=\"\\mathbf{\\frac{-3}{4}}\" 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><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-3}{5}}\" alt=\"\\mathbf{\\frac{-3}{5}}\" align=\"absmiddle\" \/>, <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{-1}{5}}\" alt=\"\\mathbf{\\frac{-1}{5}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">The given rational numbers are in form of like fraction,<br \/>\n<\/span><span style=\"color: #000000;\">Hence, <\/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;&lt;&amp;space;\\frac{-2}{5}&amp;space;&lt;\\frac{-1}{5}\" alt=\"\\frac{-3}{5} &lt; \\frac{-2}{5} &lt;\\frac{-1}{5}\" align=\"absmiddle\" \/><\/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{-1}{3}}\" alt=\"\\mathbf{\\frac{-1}{3}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-2}{9}}\" alt=\"\\mathbf{\\frac{-2}{9}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-4}{3}}\" alt=\"\\mathbf{\\frac{-4}{3}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">LCM of 3, 9, and 3 is 9<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-1\\times&amp;space;3}{3\\times&amp;space;3}\" alt=\"\\frac{-1\\times 3}{3\\times 3}\" align=\"absmiddle\" \/>, <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{-4\\times&amp;space;3}{3\\times&amp;space;3}\" alt=\"\\frac{-4\\times 3}{3\\times 3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{9}\" alt=\"\\frac{-3}{9}\" align=\"absmiddle\" \/>, <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{-12}{9}\" alt=\"\\frac{-12}{9}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">Since <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-12}{9}\" alt=\"\\frac{-12}{9}\" align=\"absmiddle\" \/><\/span><span style=\"color: #000000;\">\u00a0&lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{9}\" alt=\"\\frac{-3}{9}\" align=\"absmiddle\" \/>\u00a0&lt; <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=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">Hence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4}{3}\" alt=\"\\frac{-4}{3}\" align=\"absmiddle\" \/><\/span><span style=\"color: #000000;\"> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-1}{3}\" alt=\"\\frac{-1}{3}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-2}{9}\" alt=\"\\frac{-2}{9}\" align=\"absmiddle\" \/><\/span><\/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{-3}{7}}\" alt=\"\\mathbf{\\frac{-3}{7}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-3}{2}}\" alt=\"\\mathbf{\\frac{-3}{2}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-3}{4}}\" alt=\"\\mathbf{\\frac{-3}{4}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">LCM of 7, 2, and 4 is 28<\/span><\/p>\n<p><span style=\"font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3\\times&amp;space;4}{7\\times&amp;space;4}\" alt=\"\\frac{-3\\times 4}{7\\times 4}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3\\times&amp;space;14}{2\\times&amp;space;14}\" alt=\"\\frac{-3\\times 14}{2\\times 14}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3\\times&amp;space;7}{4\\times&amp;space;7}\" alt=\"\\frac{-3\\times 7}{4\\times 7}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-12}{28}\" alt=\"\\frac{-12}{28}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-42}{28}\" alt=\"\\frac{-42}{28}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-21}{28}\" alt=\"\\frac{-21}{28}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">Since <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-42}{28}\" alt=\"\\frac{-42}{28}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-21}{28}\" alt=\"\\frac{-21}{28}\" align=\"absmiddle\" \/> &lt;<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-12}{28}\" alt=\"\\frac{-12}{28}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-family: georgia, palatino, serif;\"><span style=\"color: #000000;\">Hence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{2}\" alt=\"\\frac{-3}{2}\" align=\"absmiddle\" \/><\/span><span style=\"color: #000000;\"> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{4}\" alt=\"\\frac{-3}{4}\" align=\"absmiddle\" \/> &lt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-3}{7}\" alt=\"\\frac{-3}{7}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 7 Mathematics\u00a0 Chapter &#8211; 9 (Rational Numbers) The NCERT Solutions in English Language for Class 7 Mathematics Chapter &#8211; 9 Rational Numbers Exercise 9.1 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter : 9 Rational Numbers NCERT Solution Class 7 Maths Exercise &#8211; 9.2 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[219],"tags":[336,337,283,5],"class_list":["post-2033","post","type-post","status-publish","format-standard","hentry","category-class-7-maths","tag-ncert-class-7-maths-chapter-9-rational-numbers-in-english","tag-ncert-solutions-class-7-maths-chapter-9-in-english","tag-ncert-solutions-class-7-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 7 Mathematics\u00a0Chapter - 9 (Rational Numbers)The NCERT Solutions in English Language for Class 7 Mathematics Chapter - 9 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