Question

Which of the following options is correct?
(1) Every integer and fraction is a rational number.
(2) A rational number $\frac{p}{q}$ is positive if p and q are either both positive or both negative.

(3) A rational number $\frac{p}{q}$ is negative if one of p and q is positive and other is negative.
(4) If there are two rational numbers with same denominator, then the one with the larger numerator is larger than the other.

• A. Both $1$ and $4$ are incorrect
• B. Both $2$ and $3$ are incorrect
• C. Only $1$ is correct
• D. All are correct

Answer 1

The correct option is D All are correct

$\left(1\right)$ Every integer and fraction is a rational number - True

$\left(2\right)$ A rational number $\frac{p}{q}$ is positive if $p$ and$q$ are either both positive or both negative - True.

$\left(3\right)$ A rational number $\frac{p}{q}$ is negative if one of $p$ and $q$ is positive and other is negative - True.

$\left(4\right)$ If there are two rational numbers with same denominator, then the one with the larger numerator is larger numerator is larger than the other - True

$\therefore$ All the statements are correct.