Question

The product of two rational numbers is always a ……………………. Number.

Answer 1

Hint: In this question we have to comment on the product of two rational numbers. A rational number is one which can be represented in the form $\dfrac{a}{b}$ such that $b \ne 0$. Try to think of another rational number and multiply it with the first general rational number assumed. Now use this product obtained to check whether it’s a whole number, irrational or a rational number.

Complete step-by-step answer:
As we know a rational number is a number which is represented in the form of $\dfrac{a}{b}$, where $b \ne 0$ and a and b don’t have any common factors except 1.
Then it can be represented as a fraction of two integers.
Let the lowest terms representation of the first rational number be $\dfrac{p}{q}$, where$q \ne 0$.
And the lowest term representation of the second rational number is $\dfrac{l}{m}$, where$m \ne 0$.
So the product of these two rational numbers is $ = \dfrac{{pl}}{{qm}}$, where$qm \ne 0$.
Let $pl = x,qm = y$.
$ \Rightarrow \dfrac{{pl}}{{qm}} = \dfrac{x}{y}$, where $y \ne 0$ and x and y is the lowest term representation which is a rational number.
Therefore the product of two rational numbers is always a rational number.
Hence option (A) is correct.

Note: Whenever we face such type of problems the key concept is to have the basic understanding of rational number (its definition is being mentioned while performing the solution), irrational number (numbers which is not of the form $\dfrac{a}{b}$ where $b \ne 0$) and whole numbers (a number without fractions, basically an integer).