{"id":27568,"date":"2021-07-01T11:31:31","date_gmt":"2021-07-01T06:01:31","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=27568"},"modified":"2021-07-01T11:31:31","modified_gmt":"2021-07-01T06:01:31","slug":"ncert-solutions-for-class-7-maths-chapter-9-ex-9-1","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-7-maths-chapter-9-ex-9-1\/","title":{"rendered":"NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Ex 9.1"},"content":{"rendered":"

These 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>\n

NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Exercise 9.1<\/h2>\n

\"NCERT<\/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\"NCERT
\n\"NCERT<\/p>\n

(ii) -2 and -1
\n\"NCERT
\nare the five rational numbers between -2 and -1<\/p>\n

(iii) \\(\\frac{-4}{5}\\) and \\(\\frac{-2}{3}\\)
\n\"NCERT
\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\"NCERT<\/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\"NCERT
\nThus, we observe a pattern in these numbers.
\nThe next four more rational numbers are
\n\"NCERT
\nThe four required rational numbers are \\(\\frac{-15}{25}, \\frac{-18}{30}, \\frac{-21}{35}\\) and \\(\\frac{-24}{40}\\)
\n\"NCERT
\nThus, we observe a pattern in these numbers.
\nNext Four rational numbers are
\n\"NCERT
\nThe next four required rational numbers are \\(\\frac{-4}{16}, \\frac{-5}{20}, \\frac{-6}{24}\\) and \\(\\frac{-7}{28}\\)<\/p>\n

\"NCERT
\nThus, we observe a pattern in these numbers
\nThe next four rational numbers would be
\n\"NCERT
\nThe required four rational numbers are \\(\\frac{5}{-30}, \\frac{6}{-36} ; \\frac{7}{-42}\\) and \\(\\frac{8}{-48}\\)<\/p>\n

\"NCERT
\nThus, we observe a pattern in these numbers
\nFour more rational numbers would be
\n\"NCERT
\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\"NCERT<\/p>\n

(ii) Four rational numbers equivalent to
\n\"NCERT<\/p>\n

(iii) Four rational numbers equivalent to
\n\"NCERT
\n\"NCERT<\/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\"NCERT<\/p>\n

\"NCERT<\/p>\n

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\"NCERT
\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\"NCERT
\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

\"NCERT<\/p>\n

(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\"NCERT
\n\"NCERT
\nAnswer:
\n\\(\\frac{-7}{6}\\) is a negative rational number. 6
\n\"NCERT<\/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\"NCERT<\/p>\n

\"NCERT<\/p>\n

\"NCERT
\nare negative rational numbers.
\nL.C.M of 8 and 16 is 16.
\n\"NCERT<\/p>\n

(iv) \\(\\frac{-8}{5}\\) and \\(\\frac{-7}{4}\\) are negative rational numbers.
\nLCM of 5 and 4 = 20
\n\"NCERT<\/p>\n

(v) \\(\\frac{1}{-3}\\) and \\(\\frac{-1}{4}\\) negative rational numbers.
\nL.C.M of 3 and 4 is 12.
\n\"NCERT<\/p>\n

(vi) \\(\\frac{5}{-11}\\) and \\(\\frac{-5}{11}\\) are negative rational numbers.
\n\"NCERT<\/p>\n

(vii) \\(\\frac{-7}{6}\\) is a negative integer since 0 is 6
\ngreater than every negative number.
\n\"NCERT<\/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\"NCERT
\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\"NCERT
\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\"NCERT
\n\\(\\frac{2}{-3}>\\frac{-3}{4}\\)
\nThus, the rational number \\(\\frac{2}{-3}\\) is greater.<\/p>\n

\"NCERT<\/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\"NCERT
\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\"NCERT
\nThus, the ascending order is
\n\\(\\frac{-4}{3}, \\frac{-1}{3}, \\frac{-2}{9}\\)<\/p>\n

\"NCERT<\/p>\n

(iii) \\(\\frac{-3}{7}, \\frac{-3}{2}, \\frac{-3}{4}\\)
\nL.C.M of 7, 2 and 4 is 28
\n\"NCERT<\/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

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NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers Exercise 9.1 Question 1. 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