Question

Is $\dfrac{3}{{ - 2}}$ a rational number? If so, how do you write it in a form conforming to the definition of a rational number (that is, denominator as a positive integer)?

Answer 1

Hint:A rational number is not just a normal fraction. A number that can be written in a form $\dfrac{p}{q}$ where the denominator is never equal to zero. But we can say that a rational number is in its standard form only when the denominator is always greater than zero, numerator can be greater or less than or equal to zero. To convert a number into a standard rational number, we multiply both the numerator and denominator with -1.

Complete step by step answer:
No, $\dfrac{3}{{ - 2}}$ is not a rational number since the denominator is less than zero.In Order to convert it into a standard rational number, we multiply both the numerator and denominator with -1.
$\dfrac{{3 \times ( - 1)}}{{ - 2 \times ( - 1)}} = \dfrac{{ - 3}}{2}$
Now, this is a standard rational number since the denominator is greater than zero.

Note:Remembering the definition of rational number and its standard form will help us solve this question. Along with that, there is another rule for a standard rational number. That is: the common divisor between the numerator and denominator should be 1. Inorder to convert it into standard form, we have to find their greatest common divisor and perform the division of each numerator and denominator.