NCERT Solutions for Class 7 Maths<\/a> Chapter 9 Rational Numbers Ex 9.1 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\nNCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Exercise 9.1<\/h2>\n <\/p>\n
Question 1. \nList five rational numbers between \n(i) -1 and 0 \n(ii) -2 and -1 \n(iii) \\(\\frac{-4}{5}\\) and \\(\\frac{-2}{3}\\) \n(iv) \\(\\frac{-1}{2}\\) and \\(\\frac{2}{3}\\) \nAnswer: \n(i) -1 and 0 \n \n <\/p>\n
(ii) -2 and -1 \n \nare the five rational numbers between -2 and -1<\/p>\n
(iii) \\(\\frac{-4}{5}\\) and \\(\\frac{-2}{3}\\) \n \nThe five rational numbers are \n\\(\\frac{-47}{60}<\\frac{-23}{30}<\\frac{-3}{4}<\\frac{-11}{15} \\text { and } \\frac{-43}{60}\\)<\/p>\n
(iv) \\(\\frac{-1}{2}\\) and \\(\\frac{2}{3}\\) \nL. C. M of 2 and 3 is 6 \n <\/p>\n
Question 2. \nWrite four more rational numbers in each of the following patterns. \n(i) \\(\\frac{-3}{5}, \\frac{-6}{10}, \\frac{-9}{15}, \\frac{-12}{20}\\) ……………… \n(ii) \\(\\frac{-1}{4}, \\frac{-2}{8}, \\frac{-3}{12}\\) ……………… \n(iii) \\(\\frac{-1}{6}, \\frac{2}{-12}, \\frac{3}{-18}, \\frac{4}{-24}\\) ……………… \n(iv) \\(\\frac{-2}{3}, \\frac{2}{-3}, \\frac{4}{-6}, \\frac{6}{-9}\\) ……………… \nAnswer: \n \nThus, we observe a pattern in these numbers. \nThe next four more rational numbers are \n \nThe four required rational numbers are \\(\\frac{-15}{25}, \\frac{-18}{30}, \\frac{-21}{35}\\) and \\(\\frac{-24}{40}\\) \n \nThus, we observe a pattern in these numbers. \nNext Four rational numbers are \n \nThe next four required rational numbers are \\(\\frac{-4}{16}, \\frac{-5}{20}, \\frac{-6}{24}\\) and \\(\\frac{-7}{28}\\)<\/p>\n
\nThus, we observe a pattern in these numbers \nThe next four rational numbers would be \n \nThe required four rational numbers are \\(\\frac{5}{-30}, \\frac{6}{-36} ; \\frac{7}{-42}\\) and \\(\\frac{8}{-48}\\)<\/p>\n
\nThus, we observe a pattern in these numbers \nFour more rational numbers would be \n \nThe required four rational numbers are \\(\\frac{8}{-12}, \\frac{10}{-15} ; \\frac{12}{-18}\\) and \\(\\frac{14}{-21}\\)<\/p>\n
Question 3. \nGive four rational numbers equivalent to: \n(i) \\(\\frac{-2}{7}\\) \n(ii) \\(\\frac{5}{-3}\\) \n(iii) \\(\\frac{4}{9}\\) \nAnswer: \n(i) Four rational numbers equivalent to \n <\/p>\n
(ii) Four rational numbers equivalent to \n <\/p>\n
(iii) Four rational numbers equivalent to \n \n <\/p>\n
Question 4. \nDraw the number line and represent the following rational numbers on it: \n(i) \\(\\frac{3}{4}\\) \n(ii) \\(\\frac{-5}{8}\\) \n(iii) \\(\\frac{-7}{4}\\) \n(iv) \\(\\frac{7}{8}\\) \nAnswer: \n <\/p>\n
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Question 5. \nThepointsP,Q,RS,T,U,AandBonthe number line are such that, TR = RS = SU \nand AP = PQ = QB. Name the rational numbers represented by P, Q, R, and S. \n \nAnswer: \nSince AP = PQ = QB \nDistance between 2 and 3 is divided into 3 equal parts. \nSimilarly, distance between -2 and -1 is also divided into three equal parts. \nP represents the rational number \n\\(\\left(2+\\frac{1}{3}\\right) \\text { i.e. } \\frac{7}{3}\\) \nQ represents the rational number \n\\(\\left(2+\\frac{2}{3}\\right) \\text { i.e. } \\frac{8}{3}\\) \nR represents the rational number \n\\(\\left(-1-\\frac{1}{3}\\right) \\text { i.e. } \\frac{-4}{3}\\) \nS represents the rational number \n\\(\\left(-1-\\frac{2}{3}\\right) \\text { ie } \\frac{-5}{3}\\)<\/p>\n
Question 6. \nWhich of the following pairs represent the same rational number? \n(i) \\(\\frac{-7}{21}\\) and \\(\\frac{3}{9}\\) \n(ii) \\(\\frac{-16}{20}\\) and \\(\\frac{20}{-25}\\) \n(iii) \\(\\frac{-2}{-3}\\) and \\(\\frac{2}{3}\\) \n(iv) \\(\\frac{-3}{5}\\) and \\(\\frac{-12}{20}\\) \n(v) \\(\\frac{8}{-5}\\) and \\(\\frac{-24}{15}\\) \n(vi) \\(\\frac{1}{3}\\) and \\(\\frac{-1}{9}\\) \n(vii) \\(\\frac{-5}{-9}\\) and \\(\\frac{5}{-9}\\) \nAnswer: \n(i) \\(\\frac{-7}{21}\\) and \\(\\frac{3}{9}\\) \nHere \\(\\frac{-7}{21}\\) is a negative rational number and \\(\\frac{3}{9}\\) is a positive rational number. \n\\(\\frac{-7}{21}=\\frac{-1}{3} ; \\frac{3}{9}=\\frac{1}{3} ; \\frac{-7}{21} \\neq \\frac{3}{9}\\) \nThus, \\(\\frac{-7}{21}\\) and \\(\\frac{3}{9}\\) does not represent the same rational number.<\/p>\n
(ii) \\(\\frac{-16}{20}\\) and \\(\\frac{20}{-25}\\) \nWe have \\(\\frac{-16}{20}\\)= \\(\\frac{-4}{5}\\) \n \nThus, \\(\\frac{-16}{20}\\) and \\(\\frac{20}{-25}\\) represent the same rational number.<\/p>\n
(iii) \\(\\frac{-2}{-3}\\) and \\(\\frac{2}{3}\\) \n\\(\\frac{-2}{-3}=\\frac{+2}{3} ; \\frac{2}{3}=\\frac{2}{3}\\) \nThus, \\(\\frac{-2}{-3}\\) and \\(\\frac{2}{3}\\) represent the same rational number.<\/p>\n
(iv) \\(\\frac{-3}{5}\\) and \\(\\frac{-12}{20}\\) \nWe have, \\(\\frac{-3}{5}=\\frac{-3}{5} ; \\frac{-12}{20}=\\frac{-3}{5}\\) \nSo, \\(\\frac{-3}{5}=\\frac{-12}{20}\\) \nThus \\(\\frac{-3}{5}\\) and \\(\\frac{-12}{20}\\) represent the same rational number.<\/p>\n
(v) \\(\\frac{8}{-5}\\) and \\(\\frac{-24}{15}\\) \nWe have, \\(\\frac{8}{-5}=\\frac{-8}{5} ; \\frac{-24}{15}=\\frac{-8}{5}\\) \nSo, \\(\\frac{8}{-5}\\) = \\(\\frac{-24}{15}\\) \nThus \\(\\frac{8}{-5}\\) and \\(\\frac{-24}{15}\\) represent the same rational number.<\/p>\n
(vi) \\(\\frac{1}{3}\\) and \\(\\frac{-1}{9}\\) \nHere \\(\\frac{1}{3}\\) is positive integer and \\(\\frac{-1}{9}\\) is a negative integer. \n\u2234 \\(\\frac{1}{3} \\neq \\frac{-1}{9}\\) \nThus \\(\\frac{1}{3}\\) and \\(\\frac{-1}{9}\\) does not represent the same rational number.<\/p>\n
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(vii) \\(\\frac{-5}{-9}\\) and \\(\\frac{5}{-9}\\) \n\\(\\frac{-5}{-9}\\) and \\(\\frac{5}{-9}\\) is a positive integer. \nand \\(\\frac{-5}{-9}\\) = \\(\\frac{5}{-9}\\) is a negative integer \n\u2234 \\(\\frac{-5}{-9} \\neq \\frac{5}{-9}\\) \nThus \\(\\frac{-5}{-9}\\) and \\(\\frac{5}{-9}\\) do not represent tha same rational number.<\/p>\n
Question 7. \nRewrite the following rational numbers in the simplest form: \n(i) \\(\\frac{-8}{6}\\) \n(ii) \\(\\frac{25}{45}\\) \n(iii) \\(\\frac{-44}{72}\\) \n(iv) \\(\\frac{-8}{10}\\) \nAnswer: \n(i) \\(\\frac{-8}{6}\\) \n\\(\\frac{-8}{6}=\\frac{-4}{3}\\) (Divide both sides by 2) \nThe simplest form is \\(\\frac{-4}{3}\\)<\/p>\n
(ii) \\(\\frac{25}{45}\\) \n\\(\\frac{25}{45}=\\frac{5}{9}\\) (Divide both sides by 5) \nThe simplest form is \\(\\frac{5}{9}\\)<\/p>\n
(iii) \\(\\frac{-44}{72}\\) \n\\(\\frac{-44}{72}=\\frac{-11}{18}\\) \nDividing both sides by 4) \nThe simplest \\(\\frac{-11}{18}\\)<\/p>\n
(iv) \\(\\frac{-8}{10}\\) \n\\(\\frac{-8}{10}=\\frac{-4}{5}\\) (Dividing both sides by 2) \nThe simplest form is \\(\\frac{-4}{5}\\)<\/p>\n
Question 8. \nFill in the boxes with the correct symbol out of > , <, and = \n \n \nAnswer: \n\\(\\frac{-7}{6}\\) is a negative rational number. 6 \n <\/p>\n
(ii) \\(\\frac{-4}{5} \\text { and } \\frac{-5}{7}\\) \nare negative rational numbers. \nL.C.M of 5 and 7 is 35. \n <\/p>\n
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\nare negative rational numbers. \nL.C.M of 8 and 16 is 16. \n <\/p>\n
(iv) \\(\\frac{-8}{5}\\) and \\(\\frac{-7}{4}\\) are negative rational numbers. \nLCM of 5 and 4 = 20 \n <\/p>\n
(v) \\(\\frac{1}{-3}\\) and \\(\\frac{-1}{4}\\) negative rational numbers. \nL.C.M of 3 and 4 is 12. \n <\/p>\n
(vi) \\(\\frac{5}{-11}\\) and \\(\\frac{-5}{11}\\) are negative rational numbers. \n <\/p>\n
(vii) \\(\\frac{-7}{6}\\) is a negative integer since 0 is 6 \ngreater than every negative number. \n <\/p>\n
Question 9. \nWhich is greater in each of the following? \n(i) \\(\\frac{2}{3}, \\frac{5}{2}\\) \n(ii) \\(\\frac{-5}{6}, \\frac{-4}{3}\\) \n(iii) \\(\\frac{-3}{4}, \\frac{2}{-3}\\) \n(iv) \\(\\frac{-1}{4}, \\frac{1}{4}\\) \n(v) \\(-3 \\frac{2}{7} ;-3 \\frac{4}{5}\\) \nAnswer: \n(i) \\(\\frac{2}{3}, \\frac{5}{2}\\) \nL.C.M of 2 and 3 is 6 \n \nThus \\(\\frac{5}{2}\\) is greater rational number.<\/p>\n
(ii) \\(\\frac{-5}{6}, \\frac{-4}{3}\\) \nL.C.M of 6 and 3 is 6 \n \nThus \\(\\frac{-5}{6}\\) is greater rational number.<\/p>\n
(iii) \\(\\frac{-3}{4}, \\frac{2}{-3}\\) \nL.C.M of 4 and 3 is 12 \n \n\\(\\frac{2}{-3}>\\frac{-3}{4}\\) \nThus, the rational number \\(\\frac{2}{-3}\\) is greater.<\/p>\n
<\/p>\n
(iv) \\(\\frac{-1}{4}, \\frac{1}{4}\\) \nsince a positive rational number is always greater than a negative rational number. \n\\(\\frac{1}{4}>\\frac{-1}{4}\\) \nThus, greater rational number is \\(\\frac{1}{4}\\)<\/p>\n
(v) \\(-3 \\frac{2}{7} ;-3 \\frac{4}{5}\\) \n \nThus, rational number -3\\(\\frac{2}{7}\\) is greater.<\/p>\n
Question 10. \nWrite the following rational numbers in ascending order. \n(i) \\(\\frac{-3}{5}, \\frac{-2}{5}, \\frac{-1}{5}\\) \n(ii) \\(\\frac{-1}{3}, \\frac{-2}{9}, \\frac{-4}{3}\\) \n(iii) \\(\\frac{-3}{7}, \\frac{-3}{2}, \\frac{-3}{4}\\) \nAnswer: \n(i) \\(\\frac{-3}{5}, \\frac{-2}{5}, \\frac{-1}{5}\\) \n\\(-\\frac{3}{5}<-\\frac{2}{5}<-\\frac{1}{5}\\) \nThe ascending order is \\(-\\frac{3}{5},-\\frac{2}{5},-\\frac{1}{5}\\)<\/p>\n
(ii) \\(\\frac{-1}{3}, \\frac{-2}{9}, \\frac{-4}{3}\\) \nL.C.M of 3 and 9 is 9 \n \nThus, the ascending order is \n\\(\\frac{-4}{3}, \\frac{-1}{3}, \\frac{-2}{9}\\)<\/p>\n
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(iii) \\(\\frac{-3}{7}, \\frac{-3}{2}, \\frac{-3}{4}\\) \nL.C.M of 7, 2 and 4 is 28 \n <\/p>\n","protected":false},"excerpt":{"rendered":"
These NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Exercise 9.1 Question 1. List five rational numbers between (i) -1 and 0 (ii) -2 and -1 (iii) and (iv) and …<\/p>\n
NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"default","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","spay_email":""},"categories":[9],"tags":[],"yoast_head":"\nNCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1 - MCQ Questions<\/title>\n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\t \n\t \n\t \n