{"id":5922,"date":"2023-05-21T16:01:14","date_gmt":"2023-05-21T10:31:14","guid":{"rendered":"https:\/\/apboardsolutions.in\/?p=5922"},"modified":"2023-05-22T17:24:25","modified_gmt":"2023-05-22T11:54:25","slug":"ap-board-8th-class-maths-solutions-chapter-1-ex-1-1","status":"publish","type":"post","link":"https:\/\/apboardsolutions.in\/ap-board-8th-class-maths-solutions-chapter-1-ex-1-1\/","title":{"rendered":"AP Board 8th Class Maths Solutions Chapter 1 Rational Numbers Ex 1.1"},"content":{"rendered":"

AP State Syllabus AP Board 8th Class Maths Solutions<\/a> Chapter 1 Rational Numbers Ex 1.1 Textbook Questions and Answers.<\/p>\n

AP State Syllabus 8th Class Maths Solutions 1st Lesson Rational Numbers Exercise 1.1<\/h2>\n

\"AP<\/p>\n

Question 1.
\nName the properly Involved in the following examples.
\n\"AP
\nvii) 7a + (-7) = 0
\nviii) x + \\(\\frac{1}{x}\\) = 1(x \u2260 0)
\nix) (2 x x) + (2 x 6) = 2 x (x + 6)
\nSolution:
\ni) Additive identity
\nii) Distributive law
\niii) Multiplicative identity
\niv) Multiplicative identity
\nv) Commutative law of addition
\nvi) Closure law in multiplication
\nvii) Additive inverse
\nviii) Multiplicative inverse
\nix) Distributive<\/p>\n

\"AP<\/p>\n

Question 2.
\nWrite the additive and the multiplicative inverses of the following.
\ni) \\(\\frac{-3}{5}\\)
\nii) 1
\niii) 0
\niv) \\(\\frac{7}{9}\\)
\nv) -1
\nSolution:
\n\"AP<\/p>\n

Question 3.
\nFill in the blanks
\n\"AP
\n\"AP
\n\"AP
\nSolution:
\ni) \\(\\left(\\frac{-12}{5}\\right)\\)
\nii) \\(\\left(\\frac{4}{3}\\right)\\)
\niii) \\(\\left(\\frac{9}{11}\\right)\\)
\niv) \\(\\left(\\frac{6}{7}\\right)\\)
\nv) \\(\\left(\\frac{3}{4}, \\frac{1}{3}\\right)\\)
\nvi) 0<\/p>\n

\"AP<\/p>\n

Question 4.
\nMultiply \\(\\frac{2}{11}\\) by the reciprocal of \\(\\frac{-5}{14}\\)
\nSolution:
\nThe reciprocal of \\(\\frac{-5}{14}\\) is \\(\\frac{-14}{5}\\)
\n( \u2235 \\(\\left(\\frac{-5}{14}\\right) \\times\\left(\\frac{-14}{5}\\right)=1\\) )
\n\u2234 The product of \\(\\frac{2}{11}\\) and \\(\\frac{-14}{5}\\) is
\n\\(\\frac{2}{11} \\times\\left(\\frac{-14}{5}\\right)=\\frac{-28}{55}\\)<\/p>\n

Question 5.
\nWhich properties can be used computing \\(\\frac{2}{5} \\times\\left(5 \\times \\frac{7}{6}\\right)+\\frac{1}{3} \\times\\left(3 \\times \\frac{4}{11}\\right)\\)
\nSolution:
\nThe following properties are involved in the product of
\n\\(\\frac{2}{5} \\times\\left(5 \\times \\frac{7}{6}\\right)+\\frac{1}{3} \\times\\left(3 \\times \\frac{4}{11}\\right)\\)
\ni) Multiplicative associative property.
\nii) Multiplicative inverse.
\niii) Multiplicative identity.
\niv) Closure with addition<\/p>\n

Question 6.
\nVerify the following
\n\\(\\left(\\frac{5}{4}+\\frac{-1}{2}\\right)+\\frac{-3}{2}=\\frac{5}{4}+\\left(\\frac{-1}{2}+\\frac{-3}{2}\\right)\\)
\nSolution:
\n\"AP<\/p>\n

\"AP<\/p>\n

Question 7.
\nEvaluate \\(\\frac{3}{5}+\\frac{7}{3}+\\left(\\frac{-2}{5}\\right)+\\left(\\frac{-2}{3}\\right)\\) after rearrangement.
\nSolution:
\n\"AP
\nLet x = \\(1.2 \\overline{4}\\)
\n\u21d2 x = 1.244……. …………………(1)
\nHere periodicity of equation (1) is 1. So
\nit should be multiplied by 10 on both
\nsides.
\n\u21d2 10 x x = 10 x 1.244
\n10x = 12.44 …………..(2)
\n\"AP<\/p>\n

\"AP<\/p>\n

Question 8.
\nSubtract
\n(i) \\(\\frac{3}{4}\\) from \\(\\frac{1}{3}\\)
\n(ii) \\(\\frac{-32}{13}\\) from 2
\n(iii) -7 from \\(\\frac{-4}{7}\\)
\nSolution:
\n\"AP
\n\"AP<\/p>\n

Question 9.
\nWhat numbers should be added to \\(\\frac{-5}{8}\\) so as to get \\(\\frac{-3}{2}\\) ?
\nSolution:
\nLet the number to be add ‘x’ say
\n\"AP
\n\u2234 \\(\\frac{-7}{8}\\) should be added to \\(\\frac{-5}{8}\\) then we will get \\(\\frac{-3}{2}\\)<\/p>\n

Question 10.
\nThe sum of two rational numbers is 8 If one of the numbers is \\(\\frac{-5}{6}\\) find the other.
\nLet the second number be ‘x’ say
\n\u21d2 \\(x+\\left(\\frac{-5}{6}\\right)=8\\)
\n\u21d2\\(8+\\frac{5}{6}=\\frac{48+5}{6}=\\frac{53}{6}\\)
\n\u2234 The other number (x) = \\(\\frac{53}{6}\\)<\/p>\n

Question 11.
\nIs subtraction associative in rational numbers? Explain with an example.
\nSolution:
\nLet \\(\\frac{1}{2}, \\frac{3}{4}, \\frac{-5}{4}\\) are any 3 rational numbers.
\nAssociative property under subtraction
\na – (b – c) = (a – b) – c
\n\"AP
\n\u2234 L.H.S. \u2260 R.H.S.
\n\u2234 a – (b – c) \u2260 (a – b) – c
\n\u2234 Subtraction is not an associative in rational numbers.<\/p>\n

\"AP<\/p>\n

Question 12.
\nVerify that – (-x) = x for
\n(i) x = \\(\\frac{2}{15}\\)
\n(ii) x = \\(\\frac{-13}{15}\\)
\nSolution:
\n\"AP<\/p>\n

Question 13.
\nWrite-
\n(i) The set of numbers which do not have any additive identity
\n(ii) The rational number that does not have any reciprocal
\n(iii) The reciprocal of a negative rational number.
\nSolution:
\ni) Set of natural numbers \u2019N’ doesn’t possesses the number ‘0’.
\nii) The rational number ‘0’ has no multiplicative inverse.
\n[ \u2235 1\/0 is not defined]
\niii) The reciprocal of a negative rational number is a negative rational number.
\nEx : Reciprocal of \\(\\frac{-2}{5}=\\frac{-5}{2}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Syllabus AP Board 8th Class Maths Solutions Chapter 1 Rational Numbers Ex 1.1 Textbook Questions and Answers. AP State Syllabus 8th Class Maths Solutions 1st Lesson Rational Numbers Exercise 1.1 Question 1. Name the properly Involved in the following examples. vii) 7a + (-7) = 0 viii) x + = 1(x \u2260 0) … Read more<\/a><\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/5922"}],"collection":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/comments?post=5922"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/5922\/revisions"}],"predecessor-version":[{"id":40623,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/posts\/5922\/revisions\/40623"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/media?parent=5922"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/categories?post=5922"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.in\/wp-json\/wp\/v2\/tags?post=5922"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}