{"id":1658,"date":"2022-11-02T15:15:30","date_gmt":"2022-11-02T15:15:30","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=1658"},"modified":"2022-11-02T15:15:30","modified_gmt":"2022-11-02T15:15:30","slug":"ncert-solutions-class-7-maths-chapter-2-fractions-and-decimals-ex-2-1","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-2-fractions-and-decimals-ex-2-1\/","title":{"rendered":"NCERT Solutions Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.1"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 7 Maths<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 2 (Fractions and Decimals)<\/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; 2 Fractions and Decimals <\/strong>Exercise 2.1 has been provided here to help the students in solving the questions from this exercise.<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Chapter : 2 Fractions and Decimals<\/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-2-fractions-and-decimals-ex-2-2\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 7 Maths Exercise &#8211; 2.2<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-2-fractions-and-decimals-ex-2-3\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 7 Maths Exercise &#8211; 2.3<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-2-fractions-and-decimals-ex-2-4\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 7 Maths Exercise &#8211; 2.4<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-2-fractions-and-decimals-ex-2-5\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 7 Maths Exercise &#8211; 2.5<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-2-fractions-and-decimals-ex-2-6\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 7 Maths Exercise &#8211; 2.6<\/a><\/span><\/li>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-2-fractions-and-decimals-ex-2-7\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 7 Maths Exercise &#8211; 2.7<\/a><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 2.1<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. Solve:<br \/>\n<\/strong><strong>(i) 2 \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{3}{5}}\" alt=\"\\mathbf{\\frac{3}{5}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) 4 + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{7}{8}}\" alt=\"\\mathbf{\\frac{7}{8}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{3}{5}&amp;space;+&amp;space;\\frac{2}{7}}\" alt=\"\\mathbf{\\frac{3}{5} + \\frac{2}{7}}\" align=\"absmiddle\" \/>\u00a0<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iv) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{9}{11}&amp;space;-&amp;space;\\frac{4}{15}}\" alt=\"\\mathbf{\\frac{9}{11} - \\frac{4}{15}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(v) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{7}{10}&amp;space;+&amp;space;\\frac{2}{5}&amp;space;+&amp;space;\\frac{3}{2}}\" alt=\"\\mathbf{\\frac{7}{10} + \\frac{2}{5} + \\frac{3}{2}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vi) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{2\\frac{2}{3}&amp;space;+3\\frac{1}{2}}\" alt=\"\\mathbf{2\\frac{2}{3} +3\\frac{1}{2}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(vii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{8\\frac{1}{2}&amp;space;-&amp;space;3\\frac{5}{8}}\" alt=\"\\mathbf{8\\frac{1}{2} - 3\\frac{5}{8}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) 2 \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{3}{5}}\" alt=\"\\mathbf{\\frac{3}{5}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{1}&amp;space;-&amp;space;\\frac{3}{5}\" alt=\"\\frac{2}{1} - \\frac{3}{5}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">LCM of 1, 5 = 5<\/span><br \/>\n<span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2\\times&amp;space;5&amp;space;-&amp;space;3\\times&amp;space;1}{5}\" alt=\"\\frac{2\\times 5 - 3\\times 1}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{10&amp;space;-&amp;space;3}{5}\" alt=\"\\frac{10 - 3}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{5}\" alt=\"\\frac{7}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) 4 + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{7}{8}}\" alt=\"\\mathbf{\\frac{7}{8}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{1}&amp;space;+&amp;space;\\frac{7}{8}\" alt=\"\\frac{4}{1} + \\frac{7}{8}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000;\">LCM of 1, 8 = 8<\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4&amp;space;\\times&amp;space;8&amp;space;+&amp;space;7\\times1}{8}\" alt=\"\\frac{4 \\times 8 + 7\\times1}{8}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{32&amp;space;+7}{8}\" alt=\"\\frac{32 +7}{8}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{39}{8}\" alt=\"\\frac{39}{8}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?4\\frac{7}{8}\" alt=\"4\\frac{7}{8}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{3}{5}&amp;space;+&amp;space;\\frac{2}{7}}\" alt=\"\\mathbf{\\frac{3}{5} + \\frac{2}{7}}\" align=\"absmiddle\" \/>\u00a0<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">LCM of 5, 7 = 35<\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3\\times&amp;space;7&amp;space;+&amp;space;2\\times&amp;space;5}{5\\times&amp;space;7}\" alt=\"\\frac{3\\times 7 + 2\\times 5}{5\\times 7}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{21+10}{35}\" alt=\"\\frac{21+10}{35}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{31}{35}\" alt=\"\\frac{31}{35}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iv) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{9}{11}&amp;space;-&amp;space;\\frac{4}{15}}\" alt=\"\\mathbf{\\frac{9}{11} - \\frac{4}{15}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">LCM of 11, 15 = 165<\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9\\times&amp;space;15&amp;space;-&amp;space;4\\times&amp;space;11}{11\\times&amp;space;15}\" alt=\"\\frac{9\\times 15 - 4\\times 11}{11\\times 15}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{135&amp;space;-&amp;space;44}{165}\" alt=\"\\frac{135 - 44}{165}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{91}{165}\" alt=\"\\frac{91}{165}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(v) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{7}{10}&amp;space;+&amp;space;\\frac{2}{5}&amp;space;+&amp;space;\\frac{3}{2}}\" alt=\"\\mathbf{\\frac{7}{10} + \\frac{2}{5} + \\frac{3}{2}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">LCM of 10, 5 and 2 = 10<\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7\\times&amp;space;1&amp;space;+&amp;space;2\\times2&amp;space;+&amp;space;3\\times5}{10}\" alt=\"\\frac{7\\times 1 + 2\\times2 + 3\\times5}{10}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7+4+15}{10}\" alt=\"\\frac{7+4+15}{10}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{26}{10}\" alt=\"\\frac{26}{10}\" align=\"absmiddle\" \/> =\u00a0<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{13}{5}\" alt=\"\\frac{13}{5}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\frac{3}{5}\" alt=\"2\\frac{3}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vi) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{2\\frac{2}{3}&amp;space;+3\\frac{1}{2}}\" alt=\"\\mathbf{2\\frac{2}{3} +3\\frac{1}{2}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8}{3}&amp;space;+&amp;space;\\frac{7}{2}\" alt=\"\\frac{8}{3} + \\frac{7}{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">LCM of 3, 2 = 6<\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8\\times&amp;space;2&amp;space;+&amp;space;7\\times&amp;space;3}{6}\" alt=\"\\frac{8\\times 2 + 7\\times 3}{6}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{16+21}{6}\" alt=\"\\frac{16+21}{6}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{37}{6}\" alt=\"\\frac{37}{6}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?6\\frac{1}{6}\" alt=\"6\\frac{1}{6}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(vii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{8\\frac{1}{2}&amp;space;-&amp;space;3\\frac{5}{8}}\" alt=\"\\mathbf{8\\frac{1}{2} - 3\\frac{5}{8}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{17}{2}&amp;space;-&amp;space;\\frac{29}{8}\" alt=\"\\frac{17}{2} - \\frac{29}{8}\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000;\">LCM of 2, 8 = 8<\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{17\\times&amp;space;4&amp;space;-&amp;space;29\\times&amp;space;1}{8}\" alt=\"\\frac{17\\times 4 - 29\\times 1}{8}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{68-29}{8}\" alt=\"\\frac{68-29}{8}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{39}{8}\" alt=\"\\frac{39}{8}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?4\\frac{7}{8}\" alt=\"4\\frac{7}{8}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. Arrange the following in descending order:<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) <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{2}{3}}\" alt=\"\\mathbf{\\frac{2}{3}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{8}{21}}\" alt=\"\\mathbf{\\frac{8}{21}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{5}}\" alt=\"\\mathbf{\\frac{1}{5}}\" align=\"absmiddle\" \/>, <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{7}{10}}\" alt=\"\\mathbf{\\frac{7}{10}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) <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{2}{3}}\" alt=\"\\mathbf{\\frac{2}{3}}\" align=\"absmiddle\" \/>, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{8}{21}}\" alt=\"\\mathbf{\\frac{8}{21}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">LCM of 9, 3, 21 = 63<\/span><\/p>\n<p><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{9}\" alt=\"\\frac{2}{9}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2\\times&amp;space;7}{9\\times&amp;space;7}\" alt=\"\\frac{2\\times 7}{9\\times 7}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{14}{63}\" alt=\"\\frac{14}{63}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\"><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\\times&amp;space;21}{3\\times&amp;space;21}\" alt=\"\\frac{2\\times 21}{3\\times 21}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{42}{63}\" alt=\"\\frac{42}{63}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8}{21}\" alt=\"\\frac{8}{21}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8\\times&amp;space;3}{21\\times&amp;space;3}\" alt=\"\\frac{8\\times 3}{21\\times 3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{24}{63}\" alt=\"\\frac{24}{63}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Clearly,<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{42}{63}\" alt=\"\\frac{42}{63}\" align=\"absmiddle\" \/> &gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{24}{63}\" alt=\"\\frac{24}{63}\" align=\"absmiddle\" \/> &gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{14}{63}\" alt=\"\\frac{14}{63}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Hence,<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{3}\" alt=\"\\frac{2}{3}\" align=\"absmiddle\" \/> &gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{24}{63}\" alt=\"\\frac{24}{63}\" align=\"absmiddle\" \/> &gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{9}\" alt=\"\\frac{2}{9}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{5}}\" alt=\"\\mathbf{\\frac{1}{5}}\" align=\"absmiddle\" \/>, <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{7}{10}}\" alt=\"\\mathbf{\\frac{7}{10}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">LCM of 5, 7, 10 = 70<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{5}\" alt=\"\\frac{1}{5}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1\\times&amp;space;14}{5\\times14}\" alt=\"\\frac{1\\times 14}{5\\times14}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{14}{70}\" alt=\"\\frac{14}{70}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{7}\" alt=\"\\frac{3}{7}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3\\times&amp;space;10}{7\\times10}\" alt=\"\\frac{3\\times 10}{7\\times10}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{30}{70}\" alt=\"\\frac{30}{70}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{10}\" alt=\"\\frac{7}{10}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7\\times&amp;space;7}{10\\times7}\" alt=\"\\frac{7\\times 7}{10\\times7}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{49}{70}\" alt=\"\\frac{49}{70}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Clearly,<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{49}{70}\" alt=\"\\frac{49}{70}\" align=\"absmiddle\" \/> &gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{30}{70}\" alt=\"\\frac{30}{70}\" align=\"absmiddle\" \/> &gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{14}{70}\" alt=\"\\frac{14}{70}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Hence,<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{10}\" alt=\"\\frac{7}{10}\" align=\"absmiddle\" \/> &gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{7}\" alt=\"\\frac{3}{7}\" align=\"absmiddle\" \/> &gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{5}\" alt=\"\\frac{1}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. In a \u201cmagic square\u201d, the sum of the numbers in each row, in each column and along the diagonals is the same. Is this a magic square?<\/strong><\/span><\/p>\n<div class=\"table-responsive\" style=\"text-align: justify;\">\n<table class=\"table table-bordered\" style=\"width: 30%;\" border=\"1\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{11}\" alt=\"\\frac{4}{11}\" align=\"absmiddle\" \/><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{11}\" alt=\"\\frac{9}{11}\" align=\"absmiddle\" \/><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{11}\" alt=\"\\frac{2}{11}\" align=\"absmiddle\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{11}\" alt=\"\\frac{3}{11}\" align=\"absmiddle\" \/><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{11}\" alt=\"\\frac{5}{11}\" align=\"absmiddle\" \/><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{11}\" alt=\"\\frac{7}{11}\" align=\"absmiddle\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8}{11}\" alt=\"\\frac{8}{11}\" align=\"absmiddle\" \/><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{11}\" alt=\"\\frac{1}{11}\" align=\"absmiddle\" \/><\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{6}{11}\" alt=\"\\frac{6}{11}\" align=\"absmiddle\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Sum along the first row = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{11}\" alt=\"\\frac{4}{11}\" align=\"absmiddle\" \/> \u00a0+ <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{11}\" alt=\"\\frac{9}{11}\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{11}\" alt=\"\\frac{2}{11}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{11}\" alt=\"\\frac{15}{11}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Sum along the second row = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{11}\" alt=\"\\frac{3}{11}\" align=\"absmiddle\" \/> + <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{7}{11}\" alt=\"\\frac{7}{11}\" align=\"absmiddle\" \/> \u00a0= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{11}\" alt=\"\\frac{15}{11}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Sum along the third row = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8}{11}\" alt=\"\\frac{8}{11}\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{11}\" alt=\"\\frac{1}{11}\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{6}{11}\" alt=\"\\frac{6}{11}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{11}\" alt=\"\\frac{15}{11}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Sum along the first column = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{11}\" alt=\"\\frac{4}{11}\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{11}\" alt=\"\\frac{3}{11}\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8}{11}\" alt=\"\\frac{8}{11}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{11}\" alt=\"\\frac{15}{11}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Sum along the second column = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{11}\" alt=\"\\frac{9}{11}\" align=\"absmiddle\" \/> \u00a0+ <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{1}{11}\" alt=\"\\frac{1}{11}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{11}\" alt=\"\\frac{15}{11}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Sum along the third column = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{11}\" alt=\"\\frac{2}{11}\" align=\"absmiddle\" \/>\u00a0+ <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{11}\" alt=\"\\frac{7}{11}\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{6}{11}\" alt=\"\\frac{6}{11}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{11}\" alt=\"\\frac{15}{11}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Sum along the first diagonal = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{11}\" alt=\"\\frac{4}{11}\" align=\"absmiddle\" \/> + <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{6}{11}\" alt=\"\\frac{6}{11}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{11}\" alt=\"\\frac{15}{11}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Sum along the second diagonal = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{11}\" alt=\"\\frac{2}{11}\" align=\"absmiddle\" \/> + <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{8}{11}\" alt=\"\\frac{8}{11}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{11}\" alt=\"\\frac{15}{11}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Since the sum of the numbers in each row, in each column, and along the diagonals is the same, it is a magic square.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4. A rectangular sheet of paper is <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{12\\frac{1}{2}}\" alt=\"\\mathbf{12\\frac{1}{2}}\" align=\"absmiddle\" \/> cm long and <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{10\\frac{2}{3}}\" alt=\"\\mathbf{10\\frac{2}{3}}\" align=\"absmiddle\" \/>\u00a0cm wide. Find its perimeter.<br \/>\n<\/strong><strong>Solution &#8211;<br \/>\n<\/strong>Length of sheet = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?12\\frac{1}{2}\" alt=\"12\\frac{1}{2}\" align=\"absmiddle\" \/> cm = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{25}{2}\" alt=\"\\frac{25}{2}\" align=\"absmiddle\" \/> cm<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Breadth of sheet = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?10\\frac{2}{3}\" alt=\"10\\frac{2}{3}\" align=\"absmiddle\" \/> cm = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{32}{3}\" alt=\"\\frac{32}{3}\" align=\"absmiddle\" \/> cm<\/span><br \/>\n<span style=\"color: #000000;\">We know that,<\/span><br \/>\n<span style=\"color: #000000;\">Perimeter of the rectangle = 2 \u00d7 (length + breadth)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 2 \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;[&amp;space;\\frac{25}{2}&amp;space;+&amp;space;\\frac{32}{3}\\right&amp;space;]\" alt=\"\\left [ \\frac{25}{2} + \\frac{32}{3}\\right ]\" align=\"absmiddle\" \/><\/span><br \/>\n<span style=\"color: #000000;\">LCM of 2, 3 = 6<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 2 \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{25\\times&amp;space;3&amp;space;+&amp;space;32&amp;space;\\times&amp;space;2}{6}&amp;space;\\right&amp;space;)\" alt=\"\\left ( \\frac{25\\times 3 + 32 \\times 2}{6} \\right )\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 2 \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{75+64}{6}&amp;space;\\right&amp;space;)\" alt=\"\\left ( \\frac{75+64}{6} \\right )\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 2 \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{139}{6}&amp;space;\\right&amp;space;)\" alt=\"\\left ( \\frac{139}{6} \\right )\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{139}{3}\" alt=\"\\frac{139}{3}\" align=\"absmiddle\" \/> cm = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?46\\frac{1}{3}\" alt=\"46\\frac{1}{3}\" align=\"absmiddle\" \/> cm<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Hence, the perimeter of the sheet of paper is <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?46\\frac{1}{3}\" alt=\"46\\frac{1}{3}\" align=\"absmiddle\" \/> cm.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>5. Find the perimeters of (i) \u0394ABE (ii) the rectangle BCDE in this figure. Whose perimeter is greater?<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-1826\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/10\/NCERT-Solutions-Class-7-Maths-Ex-2.1-Q5.png\" alt=\"NCERT Class 7 Maths Solution\" width=\"282\" height=\"243\" \/><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<br \/>\n<\/strong>Given\u00a0 AB = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{2}\" alt=\"\\frac{5}{2}\" align=\"absmiddle\" \/> cm, AE = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?3\\frac{3}{5}\" alt=\"3\\frac{3}{5}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{18}{5}\" alt=\"\\frac{18}{5}\" align=\"absmiddle\" \/> cm,\u00a0BE = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?2\\frac{3}{4}\" alt=\"2\\frac{3}{4}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{11}{4}\" alt=\"\\frac{11}{4}\" align=\"absmiddle\" \/> cm,\u00a0ED = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{6}\" alt=\"\\frac{7}{6}\" align=\"absmiddle\" \/> cm<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) Perimeter of \u2206ABE<\/strong><\/span><br \/>\n<span style=\"color: #000000;\">Perimeter of the triangle = Sum of all sides<\/span><br \/>\n<span style=\"color: #000000;\">Perimeter of \u2206ABE = AB + BE + EA<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{2}\" alt=\"\\frac{5}{2}\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{11}{4}\" alt=\"\\frac{11}{4}\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{18}{5}\" alt=\"\\frac{18}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">The LCM of 2, 4 and 5 = 20<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5\\times10&amp;space;+&amp;space;11\\times5&amp;space;+&amp;space;18\\times4}{20}\" alt=\"\\frac{5\\times10 + 11\\times5 + 18\\times4}{20}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{50+55+72}{20}\" alt=\"\\frac{50+55+72}{20}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{177}{20}\" alt=\"\\frac{177}{20}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?8\\frac{17}{20}\" alt=\"8\\frac{17}{20}\" align=\"absmiddle\" \/> cm<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii)<\/strong> <strong>Perimeter of the rectangle BCDE<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Perimeter of the rectangle = 2 \u00d7 (length + breadth)<\/span><br \/>\n<span style=\"color: #000000;\">Perimeter of rectangle BCDE = 2 \u00d7 (BE + ED)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 2 \u00d7 [<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{11}{4}\" alt=\"\\frac{11}{4}\" align=\"absmiddle\" \/> + <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{6}\" alt=\"\\frac{7}{6}\" align=\"absmiddle\" \/>]<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">The LCM of 4, 6 = 12<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 2 \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{11&amp;space;\\times&amp;space;3&amp;space;+7\\times2}{12}\" alt=\"\\frac{11 \\times 3 +7\\times2}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 2 \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{33&amp;space;+14}{12}\" alt=\"\\frac{33 +14}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 2 \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{47}{12}\" alt=\"\\frac{47}{12}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{47}{6}\" alt=\"\\frac{47}{6}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?7\\frac{5}{6}\" alt=\"7\\frac{5}{6}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Perimeter of triangle ABE = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{177}{20}\" alt=\"\\frac{177}{20}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Perimeter of rectangle BCDE = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{47}{6}\" alt=\"\\frac{47}{6}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">LCM of 20 and 6 = 60<\/span><\/p>\n<p><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{177}{20}\" alt=\"\\frac{177}{20}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{177\\times&amp;space;3}{20\\times&amp;space;3}\" alt=\"\\frac{177\\times 3}{20\\times 3}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{531}{60}\" alt=\"\\frac{531}{60}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{47}{6}\" alt=\"\\frac{47}{6}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{47\\times&amp;space;10}{6\\times&amp;space;10}\" alt=\"\\frac{47\\times 10}{6\\times 10}\" align=\"absmiddle\" \/>\u00a0= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{470}{60}\" alt=\"\\frac{470}{60}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Clearly, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{531}{60}\" alt=\"\\frac{531}{60}\" align=\"absmiddle\" \/> &gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{470}{60}\" alt=\"\\frac{470}{60}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Hence, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{177}{20}\" alt=\"\\frac{177}{20}\" align=\"absmiddle\" \/> &gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{47}{6}\" alt=\"\\frac{47}{6}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u2234 Perimeter of \u2206ABE &gt; Perimeter of Rectangle BCDE<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>6. Salil wants to put a picture in a frame. The picture is <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{7\\frac{3}{5}}\" alt=\"\\mathbf{7\\frac{3}{5}}\" align=\"absmiddle\" \/> cm wide. To fit in the frame the picture cannot be more than <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{7\\frac{3}{10}}\" alt=\"\\mathbf{7\\frac{3}{10}}\" align=\"absmiddle\" \/>\u00a0cm wide. How much should the picture be trimmed?<br \/>\n<\/strong><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">The width of Picture = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?7\\frac{3}{5}\" alt=\"7\\frac{3}{5}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{38}{5}\" alt=\"\\frac{38}{5}\" align=\"absmiddle\" \/> cm<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Required width of a Frame = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?7\\frac{3}{10}\" alt=\"7\\frac{3}{10}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{73}{10}\" alt=\"\\frac{73}{10}\" align=\"absmiddle\" \/> cm<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u2234 The picture should be trimmed by = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{38}{5}\" alt=\"\\frac{38}{5}\" align=\"absmiddle\" \/> \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{73}{10}\" alt=\"\\frac{73}{10}\" align=\"absmiddle\" \/>\u00a0<\/span><br \/>\n<span style=\"color: #000000;\">The LCM of 5, 10 = 10<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{38&amp;space;\\times&amp;space;2&amp;space;-&amp;space;73\\times&amp;space;1}{10}\" alt=\"\\frac{38 \\times 2 - 73\\times 1}{10}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{76-73}{10}\" alt=\"\\frac{76-73}{10}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{10}\" alt=\"\\frac{3}{10}\" align=\"absmiddle\" \/> cm<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Thus, the picture should be trimmed by <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{10}\" alt=\"\\frac{3}{10}\" align=\"absmiddle\" \/>\u00a0 cm.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>7. Ritu ate <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{3}{5}}\" alt=\"\\mathbf{\\frac{3}{5}}\" align=\"absmiddle\" \/> part of an apple and the remaining apple was eaten by her brother Somu. How much part of the apple did Somu eat? Who had the larger share? By how much?<br \/>\n<\/strong><strong>Solution &#8211;<br \/>\n<\/strong>Part of apple eaten by Ritu is = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{5}\" alt=\"\\frac{3}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Part of apple eaten by Somu is = 1 \u2013 Part of apple eaten by Ritu<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= 1 \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{5}\" alt=\"\\frac{3}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">The LCM of 1, 5 = 5<\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1\\times&amp;space;5-3}{5}\" alt=\"\\frac{1\\times 5-3}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5-3}{5}\" alt=\"\\frac{5-3}{5}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{5}\" alt=\"\\frac{2}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u2234 Part of apple eaten by Somu is <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{5}\" alt=\"\\frac{2}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">So, <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{5}\" alt=\"\\frac{3}{5}\" align=\"absmiddle\" \/> &gt; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{5}\" alt=\"\\frac{2}{5}\" align=\"absmiddle\" \/> hence, Ritu ate larger size of apple.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Now, the difference between the two shares = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{5}\" alt=\"\\frac{3}{5}\" align=\"absmiddle\" \/> \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{5}\" alt=\"\\frac{2}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3-2}{5}\" alt=\"\\frac{3-2}{5}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{5}\" alt=\"\\frac{1}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Thus, Ritu\u2019s share is larger than share of Somu by <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{5}\" alt=\"\\frac{1}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>8. Michael finished colouring a picture in <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{7}{12}}\" alt=\"\\mathbf{\\frac{7}{12}}\" align=\"absmiddle\" \/> hour. Vaibhav finished colouring the same picture in <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{3}{4}}\" alt=\"\\mathbf{\\frac{3}{4}}\" align=\"absmiddle\" \/>hour. Who worked longer? By what fraction was it longer?<br \/>\n<\/strong><strong>Solution &#8211;<br \/>\n<\/strong>Time taken by Michael to colour the picture is = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{12}\" alt=\"\\frac{7}{12}\" align=\"absmiddle\" \/> hr.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Time taken by the Vaibhav to colour the picture is = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{4}\" alt=\"\\frac{3}{4}\" align=\"absmiddle\" \/> hr.<\/span><br \/>\n<span style=\"color: #000000;\">The LCM of 12, 4 = 12<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><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{7\\times&amp;space;1}{12\\times&amp;space;1}\" alt=\"\\frac{7\\times 1}{12\\times 1}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{12}\" alt=\"\\frac{7}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{4}\" alt=\"\\frac{3}{4}\" align=\"absmiddle\" \/>\u00a0 = <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{9}{12}\" alt=\"\\frac{9}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Clearly, <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{9}{12}\" alt=\"\\frac{9}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Hence, <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{3}{4}\" alt=\"\\frac{3}{4}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">Thus, Vaibhav worked for longer time. <\/span><br \/>\n<span style=\"color: #000000;\">So, Vaibhav worked longer time by = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{4}\" alt=\"\\frac{3}{4}\" align=\"absmiddle\" \/> \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{12}\" alt=\"\\frac{7}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{12}\" alt=\"\\frac{9}{12}\" align=\"absmiddle\" \/> \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{7}{12}\" alt=\"\\frac{7}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9-7}{12}\" alt=\"\\frac{9-7}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{12}\" alt=\"\\frac{2}{12}\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{6}\" alt=\"\\frac{1}{6}\" align=\"absmiddle\" \/> hour longer.<\/span><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 7 Maths Chapter &#8211; 2 (Fractions and Decimals) The NCERT Solutions in English Language for Class 7 Mathematics Chapter &#8211; 2 Fractions and Decimals Exercise 2.1 has been provided here to help the students in solving the questions from this exercise. Chapter : 2 Fractions and Decimals NCERT Solution Class 7 Maths [&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":[284,285,283,5],"class_list":["post-1658","post","type-post","status-publish","format-standard","hentry","category-class-7-maths","tag-ncert-class-7-maths-chapter-2-fractions-and-decimals-in-english","tag-ncert-solutions-class-7-maths-chapter-2-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 2 Fractions and Decimals Ex 2.1 | TheExamPillar NCERT<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-7-maths-chapter-2-fractions-and-decimals-ex-2-1\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions Class 7 Maths Chapter 2 Fractions and Decimals Ex 2.1\" \/>\n<meta property=\"og:description\" content=\"NCERT Solutions Class 7 Maths Chapter &#8211; 2 (Fractions and Decimals) The NCERT Solutions in English Language for Class 7 Mathematics Chapter &#8211; 2 Fractions and Decimals Exercise 2.1 has been provided here to help the students in solving the questions from this exercise. 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