{"id":27502,"date":"2020-07-03T11:35:53","date_gmt":"2020-07-03T06:05:53","guid":{"rendered":"https:\/\/kseebsolutions.guru\/?p=27502"},"modified":"2021-07-02T15:07:08","modified_gmt":"2021-07-02T09:37:08","slug":"kseeb-solutions-for-class-8-maths-chapter-7-additional-questions","status":"publish","type":"post","link":"https:\/\/kseebsolutions.guru\/kseeb-solutions-for-class-8-maths-chapter-7-additional-questions\/","title":{"rendered":"KSEEB Solutions for Class 8 Maths Chapter 7 Rational Numbers Additional Questions"},"content":{"rendered":"

Students can Download Maths Chapter 7 Rational Numbers Additional Questions and Answers, Notes Pdf, KSEEB Solutions for Class 8 Maths<\/a>\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.<\/p>\n

Karnataka State Syllabus Class 8 Maths Chapter 7 Rational Numbers Additional Questions<\/h2>\n

I. Fill in the blanks:<\/p>\n

Question 1.
\n(a) The number 0 is not in the set of Natural numbers<\/span>
\n(b) The least number in the set of all whole numbers is O<\/span>
\n(c) The least number in the set of al even natural numbers is 2<\/span>
\n(d) The successor of 8 in the set of all-natural numbers is 9<\/span>
\n(e) The sum of two odd integers is even<\/span>
\n(f) The product of two odd integers is odd<\/span><\/p>\n

\"KSEEB<\/p>\n

Question 2.
\nState whether the following statements are true or false.
\n(a) The set of all even natural numbers is a finite set.
\nAnswer:
\nFalse.<\/p>\n

(b) Every non-empty subset of Z has the smallest element.
\nAnswer:
\nFalse<\/p>\n

(c) Every integer can be identified with a rational number
\nAnswer:
\nTrue<\/p>\n

(d) For each rational number, one can find the ne\u00d7t rational number
\nAnswer:
\nFalse<\/p>\n

(e) There is the largest rational number
\nAnswer:
\nFalse<\/p>\n

(f) Every integer is either even or odd
\nAnswer:
\nTrue<\/p>\n

(g) Between any two rational numbers, there is an integer.
\nAnswer:
\nFalse<\/p>\n

\"KSEEB<\/p>\n

Question 3.
\nSimplify:
\n(i) 100(100 – 3) – (100 \u00d7 100 – 3)
\nSolution:
\n100(97) – (10000 – 3)
\n= 9700 – (9997) = – 297<\/p>\n

(ii) (20 – (2011 – 201) + 2011 – (201 – 20))
\n= 20 – 2011 + 201 + 2011 – 201 + 20 = 40<\/p>\n

Question 4.
\nSuppose m is an integer such that m * -1 and m \u2260 – 2. Which is larger \\(\\frac{m}{m+1} \\text { or } \\frac{m+1}{m+2} ?\\) State your reasons.
\nSolution:
\n\"KSEEB<\/p>\n

\"KSEEB<\/p>\n

Question 5.
\nDefine as operation * on the set of all rational numbers Q as follows r * s = r + s – (r \u00d7 s) for any two rational numbers r, s. Answer the following with justification.
\n(i) Is Q closed under the operatiron ?
\n(ii) Is * an associative operation on Q?
\n(iii) Is * commutative operation on Q?
\n(iv) What is a * 1 for any a in Q?
\n(v) Find two integers a \u2260 0, b \u2260 0 such that a * b = 0
\nSolution:
\n\"KSEEB
\nQ is closed under the operation *. because \u2200r, s \u2208 Q r * s = r + s – (r \u00d7 s) is also a rational number.<\/p>\n

(ii) Let r, s and p \u2208 Q
\nr * (s * p) = r * (s + p – (s \u00d7 p))<\/span>
\n= r + s + p – (s \u00d7 p)<\/span> – (r \u00d7 (s + p – (s \u00d7 p)<\/span>
\n= r + s + p – sp – (rs + rp – rsp)
\n= r + s + p – sp – rs – rp + rsp …(i)
\n(r * s) * p = r + s – (r \u00d7 s) * p<\/span>
\n= r + s – (r \u00d7 s)<\/span> + p – (r + s – (r \u00d7 s)<\/span> \u00d7 p)
\n= r + s – rs + p – (rp – sp – rsp)
\n= r + s + p – rs – rp – sp – rsp …(ii)
\nFrom (i) and (ii) r * (s * p) = (r * s) * p
\n\u2234 * is an associative operation on Q.<\/p>\n

(iii) Let r, s, \u2208 Q
\nr * s = r + s – (r \u00d7 s) = r + s – rs …(i)
\ns * r = s + r – (s \u00d7 r) = s + r – sr = r + s – rs …(ii)
\nFrom (i) and (ii) r * s = s * r
\n\u2234 * is commutative operation on Q.<\/p>\n

(vi) r * s = r + s – (r \u00d7 s)
\n\u2234 a * 1 = a + 1 – (a \u00d7 1)
\n= a + 1 – a
\na * 1 = 1<\/p>\n

(v) r * s = r + s – (r \u00d7 s)
\na * b = a + b – (a \u00d7 b)
\nif a = 2, and b = 2
\n2 * 2 = 2 + 2 – (2 \u00d7 2) = 4 – 4
\n2 * 2 = 0
\n\u2234 If a = 2 and b = 2 a * b = 0<\/p>\n

\"KSEEB<\/p>\n

Question 6.
\nFind the multiplicative inverse of the following rational numbers.
\n\\(\\frac{8}{13}\\)
\nSolution:
\n\\(\\frac{13}{8}\\)<\/p>\n

\\(\\frac{-13}{11}\\)
\nSolution:
\n\\(\\frac{-11}{13}\\)<\/p>\n

\\(\\frac{12}{17}\\)
\nSolution:
\n\\(\\frac{17}{12}\\)<\/p>\n

\\(\\frac{-101}{100}\\)
\nSolution:
\n\\(\\frac{-100}{101}\\)<\/p>\n

\\(\\frac{26}{23}\\)
\nSolution:
\n\\(\\frac{23}{26}\\)<\/p>\n

\"KSEEB<\/p>\n

Question 7.
\nWrite the following in the increasing order.
\n\\(\\frac{10}{13}, \\frac{20}{23}, \\frac{5}{6}, \\frac{40}{43}, \\frac{25}{28}, \\frac{10}{11}\\)
\nSolution:
\nTake the LCM of the denominators
\n\"KSEEB
\nLCM = 2 \u00d7 13 \u00d7 23 \u00d7 3 \u00d7 43 \u00d7 14 \u00d7 11
\n= 11879868
\n\"KSEEB<\/p>\n

Question 8.
\nWrite the following in decreasing order
\n\\(\\frac{21}{17}, \\frac{31}{27}, \\frac{13}{11}, \\frac{41}{37}, \\frac{51}{47}, \\frac{9}{8}\\)
\nSolution:
\nTake the LCM of the denominators
\nLCM = 17 \u00d7 27 \u00d7 11 \u00d7 37 \u00d7 47 \u00d7 8 = 70241688
\n\"KSEEB<\/p>\n

Question 9.
\n(a) What is the additive inverse of O?
\nSolution:
\nO<\/p>\n

(b) What is the multiplicative inverse of 1?
\nSolution:
\n1<\/p>\n

(c) Which integers have a multiplicative inverse?
\nSolution:
\n1 and -1<\/p>\n

\"KSEEB<\/p>\n

Question 10.
\nIn the set of all rational numbers, give 2 examples each illustrating the following properties.
\n(i) Associativity
\n(a)
\n\"KSEEB
\n\"KSEEB
\nAssociative property of addition in satisfied.
\n\"KSEEB
\nAssociative property of multiplication is satisfied.<\/p>\n

\"KSEEB
\nAssociative property of addition is satisfied.<\/p>\n

\"KSEEB<\/p>\n

From (i) and (ii)<\/p>\n

\"KSEEB<\/p>\n

Associative property of multiplication is satisfied.
\n(ii) Commutativity
\n(a)
\n\"KSEEB
\nComutative property of addition is satis\u00acfied.<\/p>\n

\"KSEEB
\nCommutative property of multiplication is satisfied<\/p>\n

(b)
\n\"KSEEB
\n\"KSEEB
\nCommutative property of addition is satisfied.<\/p>\n

\"KSEEB<\/p>\n

Commutative property of multiplication is satisfied.<\/p>\n

(iii) Distributivity of multiplication over addition.
\n(a)
\n\"KSEEB<\/p>\n

Multiplication is distributive over addition.<\/p>\n

(b)
\n\"KSEEB<\/p>\n

\u2234 Multiplication is distributive over addition.<\/p>\n

\"KSEEB<\/p>\n

Question 11.
\nSimplify the following using distributive property
\n(1) \\(\\frac{2}{5} \\times\\left(\\frac{1}{9}+\\frac{2}{5}\\right)\\)
\nSolution:
\n\"KSEEB<\/p>\n

(2) \\(\\frac{5}{12} \\times\\left(\\frac{25}{9}+\\frac{32}{5}\\right)\\)
\nSolution:
\n\"KSEEB
\n\"KSEEB<\/p>\n

(3) \\(\\frac{8}{9} \\times\\left(\\frac{11}{2}+\\frac{2}{9}\\right)\\)
\nSolution:
\n\"KSEEB<\/p>\n

Question 12.
\nSimplify the following:
\n(i) \\(\\left(\\frac{25}{9}+\\frac{12}{3}\\right)+\\frac{3}{5}\\)
\nSolution:
\n\"KSEEB<\/p>\n

(ii) \\(\\left(\\frac{22}{7}+\\frac{36}{5}\\right) \\times \\frac{6}{7}\\)
\nSolution:
\n\"KSEEB<\/p>\n

(iii) \\(\\left(\\frac{51}{2}+\\frac{7}{6}\\right) \\div \\frac{3}{5}\\)
\nSolution:
\n\"KSEEB<\/p>\n

(iv) \\(\\left(\\frac{16}{7}+\\frac{21}{8}\\right) \\times\\left(\\frac{15}{3}-\\frac{2}{9}\\right)\\)
\nSolution:
\n\"KSEEB<\/p>\n

Question 13.
\nWhich is the property that is there in the set of all rational numbers but which is not in the set of all integers?
\nSolution:
\nEvery non zero rational number is invertible but only + 1 are invertible integers.<\/p>\n

Question 14.
\nWhat is the value of \\(1+\\frac{1}{1+\\frac{1}{1+1}}\\)
\nSolution:
\n\"KSEEB<\/p>\n

Question 15.
\nFind the value of \\(\\left(\\frac{1}{3}-\\frac{1}{4}\\right) \/\\left(\\frac{1}{2}-\\frac{1}{3}\\right)\\)
\nSolution:
\n\"KSEEB<\/p>\n

\"KSEEB<\/p>\n

Question 16.
\nFind all rational numbers each of which is equl to its reciprocal.
\nSolution:
\nThe rational numbers + 1 and – 1 and their reciprocals are equal.<\/p>\n

Question 17.
\nA bus shuttles between two neighbouring towns every two hours. It starts from 8 AM in the morning and the last trip in at 6 PM. On one day the driver observed that the first trip had 30 passengers and each subsequent trip had one passenger less than the previous trip. How many passengers travelled on that day?
\nSolution:
\nThe number of trips = 6 The number of passengers in the first rip is 30, second trip in 29, third trip is 28 and so on
\n\u2234 No of passenger travelled on that day = 30 + 29 + 28 + 27 + 26 + 25 = 165<\/p>\n

Question 18.
\nHow many rational numbers p\/q are there between 0 and 1 for which q < P?
\nSolution:
\nThere are no rational numbers between 0 and 1 such that q < p.<\/p>\n

Question 19.
\nFind all integers such that \\(\\frac{3 n+4}{n+2}\\) is also an integer.
\nSolution:
\nLet n = 0
\n\"KSEEB
\nIt is an integer if n = 0, – 1, – 2, – 3, – 4.<\/p>\n

Question 20.
\nBy inserting parenthesis (that is brackets), you can get several values for 2 \u00d7 3 + 4 \u00d7 5 (For example ((2 \u00d7 3) + 4) \u00d7 5 is one way of inserting parenthesis) How many such values are there?
\nSolution:
\n(i) (2 \u00d7 3) + (4 \u00d7 5) = 6 + 20 = 26
\n(ii) 2 \u00d7 (3 + 4) \u00d7 5 = 2 \u00d7 7 \u00d7 5 = 70
\n(iii) 2 \u00d7 (3 + (4 \u00d7 5)) – 2 \u00d7 (3 + 20) = 2 \u00d7 23 = 46
\n(iv) ((2 \u00d7 3) + 4) \u00d7 5 = (6 + 4) \u00d7 5 = 10 \u00d7 5 = 50 There are 4 values<\/p>\n

\"KSEEB<\/p>\n

Question 21.
\nSuppose \\(\\frac{p}{q}\\) is a positive rational in its lowest form prove that \\(\\frac{1}{q}+\\frac{1}{p+q}\\) is also in its lowest form.
\nSolution:
\n\\(\\frac{p}{q}\\) is in its lowest form means p and q do not have any common factors other than 1.
\nConsider \\(\\frac{1}{q}+\\frac{1}{p+q}=\\frac{p+q+q}{q(p+q)}=\\frac{p+2 q}{q(p+q)}\\) p + 2q and q (p + q) do not have common factors other than 1 \u2234 \\(\\frac{p+2 q}{q(p+q)}\\) is in its lowest form, that means \\(\\frac{1}{q}+\\frac{1}{p+q}\\) is in its lowest form.<\/p>\n

Question 22.
\nShow that for each natural number n the fraction \\(\\frac{14 n+3}{21 n+4}\\) is in its lowest form
\nSolution:
\nIf
\n\"KSEEB
\nis in the lowest form
\nIf
\n\"KSEEB
\nis in the lowest form
\nIf
\n\"KSEEB
\nis in the lowest form
\nIf
\n\"KSEEB
\nis in the lowest form.<\/p>\n

Similarly by substituting natural numbers
\nfor n we can show that \\(\\frac{14 n+3}{21 n+4}\\) is in its lowest form.<\/p>\n

Question 23.
\nFind all integers n for which the number (n + 3) (n – 1) is also an integer.
\nSol:
\nIf n = 0, (n + 3) (n – 1) = (0 + 3) (0 – 1) = 3x-l = -3 is an integer If n = 1, (n + 3) (n – 1) = (1 + 3) (1 – 1) = 4×0 = 0 is an integer.
\nIf n = – 1, (n + 3) (n – 1) = (- 1 + 3) (- 1 – 1) = 3 (- 2) = – 6 is an integer Similarly when n is replaced by any integer we find that (n + 3) (n – 1) is also an integer
\n\u2234 n = { ……….. – 4, – 3, – 2, – 1, 0, 1, 2, 3, 4 ……….}<\/p>\n

\"KSEEB<\/p>\n","protected":false},"excerpt":{"rendered":"

Students can Download Maths Chapter 7 Rational Numbers Additional Questions and Answers, Notes Pdf, KSEEB Solutions for Class 8 Maths\u00a0helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations. Karnataka State Syllabus Class 8 Maths Chapter 7 Rational Numbers Additional Questions I. Fill in the blanks: Question 1. …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/27502"}],"collection":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/comments?post=27502"}],"version-history":[{"count":0,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/posts\/27502\/revisions"}],"wp:attachment":[{"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/media?parent=27502"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/categories?post=27502"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kseebsolutions.guru\/wp-json\/wp\/v2\/tags?post=27502"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}