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Properties of Rational Numbers

Every rationa...

Question

Every _________rational number is greater than zero.

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Solution

Since we know that a positive integer is greater than zero.
Therefore a rational with a positive numerator and denominator is greater than zero.
Thus, a positive rational number is greater than zero.
Hence, every positive rational number is greater than zero.

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Similar questions

Q. State whether the given statement is true of false:

(i) Zero is the smallest rational number.
(ii) Every integer is a rational number.
(iii) The quotient of two integers is always a rational number.
(iv) Every fraction is a rational number.
(v) Every rational number is a fraction.

Q. Mark the correct answer in each of the following:
Which of the following is not a negation of "A natural number is greater than zero".
(a) A natural number is not greater than zero
(b) It is false that a natural number is greater than zero
(c) It is false that a natural number is not greater than zero
(d) None of these

Are the following statements true or false ? Give reasons for your answer.

(i) Every whole number is a natural number.

(ii) Every integer is a rational number.

(iii) Every rational number is an integer.

(iv) Every natural number is a whole number.

(v) Every integer is a whole number.

(vi) Every rational number is a whole number.

Every negative rational number is smaller than zero.

Q. For every non-zero rational number

\frac{a}{b}

there exists a rational

\frac{c}{d}

\frac{a}{b} \times \frac{c}{d} = 1

, then the rational number

\frac{c}{d}

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Properties of Rational Numbers

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