Question

What type of number is \[\dfrac{0.25}{-0.25}\] ?

Answer 1

Hint: These type of questions are quite simple in nature and are easy to solve once we understand the key concepts behind the problem. We need to have a fair amount of fractions, number systems, rational and irrationals. In the given fraction, we see that, on the numerator and the denominator, we have the same real number but with opposite signs. We need to know the definition of rational and irrational before solving this problem. A rational fraction is one, which can be represented of the form \[\dfrac{p}{q}\] and an irrational fraction is one which cannot be represented of the form \[\dfrac{p}{q}\] . Here ‘p’ and ‘q’ are arbitrary real numbers.

Complete step-by-step answer:
Now we start off with the solution to the given problem by writing that, in the given fraction, we have a real number on both the numerator as well as on the denominator. These type of fractions are called rational fractions as they are represented of the form \[\dfrac{p}{q}\] . In this particular rational fraction, the magnitude of the value of on both the numerator and the denominator are equal however their signs are opposite. This results to a value equal to \[\dfrac{0.25}{-0.25}=-1\] which is a negative number as well as a rational number as we can represent this number in the form of \[\dfrac{p}{q}\] as \[\dfrac{-1}{1}\].

Note: Such problems require some previous knowledge of fractions and real numbers. We must remember that a fraction that can be represented of the form \[\dfrac{p}{q}\] is known as a rational fraction and the one that cannot be represented is known as an irrational fraction. Here in this problem, since we have both the numerator and the denominator of equal magnitude and of opposite sign, it yields a value equal to \[-1\] .