Question

Which of the following rational numbers is in the standard form?
(a) $\dfrac{8}{-36}$
(b) $\dfrac{-7}{53}$
(c) $\dfrac{3}{-4}$
(d) None of these

Answer 1

Hint: Check the options. The option in which numerator and denominator have the highest common factor 1 and the denominator is positive, is the rational number written in standard form.

Complete step-by-step answer:

In mathematics, rational numbers are the numbers that can be represented as $\dfrac{p}{q}$, where $p$ and $q$ are integers and $q$ must not be equal to zero. If $q$ is equal to 1 then the given rational number will become an integer, that means, every integer is a rational number. In other words, a set of integers is the subset of a set of rational numbers. The decimal expansion of a rational number always either terminates after a finite number of digits or begins to repeat the same finite sequence of digits over and over which is termed as non-terminating repeating decimal expansion.
Now, let us know about the standard form of a rational number. A rational number is said to be in the standard form, if its denominator is a positive integer and the numerator and denominator have no common factor other than one.
Now, let us come to the question. In option (a), the denominator is negative. In option (b), denominator is positive and numerator and denominator have no common factor other than 1. In option (c), the denominator is negative.
Hence, we can conclude that option (b) is the answer.

Note: We can convert any fraction or rational number into its standard form. If the denominator is negative then multiply both numerator and denominator by ($-1$). If numerator and denominator are having the highest common factor other than 1, then divide both numerator and denominator by that factor.