Fill in the blanks: (i) depicts ......... property of addition of rational numbers. (ii) The multiplicative inverse of a rational number is also called its ......... (iii) The multiplicative inverse of a negative rational number is a ......... rational number. (iv) The numbers ......... and ......... are their own reciprocals. (v) ......... = 1 (vi) ......... = 1 (vii) Among the greatest rational number is .........

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KnowledgeBoat · Accepted Answer

(i) Here the order of the two rational numbers has been changed but the sum remains the same. If are any two rational numbers, then . Hence, the given statement depicts the commutative property of addition of rational numbers. (ii) For every non-zero rational number , the rational number satisfies Hence, the multiplicative inverse of a rational number is also called its reciprocal. (iii) The multiplicative inverse is obtained by interchanging the numerator and the denominator, so the sign of the rational number does not change. For example, the multiplicative inverse of Hence, the multiplicative inverse of a negative rational number is a negative rational number. (iv) As 1 × 1 = 1 and (-1) × (-1) = 1, each of these numbers is its own reciprocal. Hence, the numbers 1 and -1 are their own reciprocals. (v) For every non-zero rational number , we have Hence, . (vi) The product of a non-zero rational number and its reciprocal is 1, so the required number is the reciprocal of . Hence, . (vii) All three rational numbers are negative and have the same numerator -5, so write them with a common denominator and compare. As -715 -455 -385, so . Hence, the greatest rational number is .

Mathematics

Rational Numbers

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