Fill in the blanks: (i) ......... is the rational number that does not have a multiplicative inverse. (ii) ......... and ......... are the rational numbers which are equal to their own reciprocals. (iii) The product of a rational number and its reciprocal is ......... (iv) The reciprocal of a positive rational number is ......... (v) The reciprocal of a negative rational number is ......... (vi) ......... is not the reciprocal of any number. (vii) The multiplicative inverse of a rational number , is .........

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KnowledgeBoat · Accepted Answer

(i) There is no rational number which when multiplied by 0 gives 1. Hence, 0 is the rational number that does not have a multiplicative inverse. (ii) As 1 × 1 = 1 and (-1) × (-1) = 1, each of these numbers is its own reciprocal. Hence, 1 and -1 are the rational numbers which are equal to their own reciprocals. (iii) For every non-zero rational number , we have . Hence, the product of a rational number and its reciprocal is 1. (iv) The reciprocal is obtained by interchanging the numerator and the denominator, so the sign of the rational number does not change. For example, the reciprocal of . Hence, the reciprocal of a positive rational number is a positive rational number. (v) The reciprocal is obtained by interchanging the numerator and the denominator, so the sign of the rational number does not change. For example, the reciprocal of . Hence, the reciprocal of a negative rational number is a negative rational number. (vi) As the product of any rational number and 0 is 0 and never 1, no rational number has 0 as its reciprocal. Hence, 0 is not the reciprocal of any number. (vii) Interchanging the numerator and the denominator of , we get . Check : Hence, the multiplicative inverse of a rational number is .

Mathematics

Rational Numbers

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