State whether each of the following statements is true or false: (i) Every whole number is a rational number. (ii) Every integer is a rational number. (iii) (iv) (v) is a negative rational number. (vi) 0 is a whole number but it is not a rational number.

Question

KnowledgeBoat · Accepted Answer

(i) Every whole number can be written as , which is of the form where are integers and . For example, Hence, the given statement is true. (ii) Every integer can be written as , which is of the form where are integers and . For example, . Hence, the given statement is true. (iii) An equivalent rational number is obtained by multiplying (or dividing) both the numerator and the denominator by the same non-zero number, not by adding the same number to both. Hence, the given statement is false. (iv) Write both the rational numbers with the LCM of their denominators as the common denominator. L.C.M. of 6 and 5 = 30 As -36 -25, so . Hence, the given statement is false. (v) A rational number is positive if its numerator and denominator are either both positive or both negative. , which is a positive rational number. Hence, the given statement is false. (vi) 0 is a whole number and it can also be written as , which is of the form where , so 0 is a rational number as well. Hence, the given statement is false.

Mathematics

State whether each of the following statements is true or false: (i) Every whole number is a rational number. (ii) Every integer is a rational number. (iii) (iv) (v) is a negative rational number. (vi) 0 is a whole number but it is not a rational number.

Rational Numbers

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