Question

In the standard form of rational numbers, the denominator is always a
A) 0
B) Negative integer
C) Positive integer
D) 1

Answer 1

Hint:The above question is based on the concept of rational numbers in fraction form. The main concept towards solving the above question is to find the correct value for the denominator so that the fraction remains rational.

Complete step by step solution:
In mathematics, the rational number expressed in standard form which means there is no common factor other than one from the numerator and denominator and the denominator is a positive integer. In general, we can write it in the form of $\dfrac{p}{q}$ where p and q are integers and q is not equal to zero then it is called as rational numbers.
We rationalize so that we get it in standard forms. In fractions it is said to be in standard form, if both the numerator and denominator is coprime. That is the common factor needs between the numerator and denominator.
This can be found by calculating Highest common factor from the numerator and denominator which should be 1. If the number is 1 then we can say that the rational number is in its standard form. And for it to be rational the denominator should be a positive integer.
Therefore, option c is correct.

Note: An important thing to note is that if both numerator and denominator is not coprime, then we can start dividing the numerator and denominator by a common factor and we keep on dividing until we get the Highest common factor as 1.
\[\dfrac{9}{{15}} = \dfrac{3}{5}\]