Question

Which of the following options hold?
(1) Every integer is a rational number and every 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 common denominator then the one with the larger numerator is larger than the other.

• A. Both 1 and 4 are correct
• 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 can be represented in form of $\frac{p}{q}$, so rational.

$\left(2\right)$ If both $p$ and $q$ are positive or negative, rational number is positive, i.e., $\frac{-p}{-q}=\frac{p}{q}=positive$

$\left(3\right)$ If either $p$ or $q$ is negative, then rational number is negative.

$\left(4\right)$ If two rational numbers having same denominator, then number having larger numerator will be larger.

For example- $\frac{4}{9}>\frac{1}{9}$

All are correct.