Question

Multiplication of two rational numbers:
A) is always a rational
B) is always a irrational
C) can be a rational or is irrational
D) None of the above

Answer 1

Hint: To solve this question we need to know about the Rational numbers. Rational number is a kind of number which is expressed as a fraction with an integer value in the numerator and in the denominator where the denominator cannot be zero. The rational number is expressed as $\dfrac{p}{q}$ where $q\ne 0$.

Complete step-by-step solution:
The question asks us, what shall be the product when two rational numbers are multiplied to each other. To solve this question we will first analyse the definition of the rational number and how it is expressed. So a rational number is expressed, basically in the form of a fraction where you may take any number as a numerator while the denominator should not be zero. To make the analysis easy, we will be considering two rational numbers which will be $\dfrac{a}{b}$ and $\dfrac{p}{q}$ , here ($b,q$ should not be zero) . Now since we are asked about the product this means we will multiply the two rational numbers given to us. On multiplying we get:
$\Rightarrow \dfrac{a}{b}\times \dfrac{p}{q}$
In the case of fractions the numerators are multiplied together while denominations are multiplied together. This forms another fraction which is:
$\Rightarrow \dfrac{ap}{bq}$
Now in the above fraction $bq$ will not be zero as both $b$ and $q$ are non- zeros.
Since, $\dfrac{ap}{bq}$ is a fraction having a denominator not equal to zero, it is a rational number.
$\therefore $ Multiplication of two rational numbers A) is always rational.

Note:Do remember whenever we solve questions like this we should take the help of examples. Examples make the solution much easier to understand. Product of two irrational numbers is sometimes irrational. Again this could be proved with the help of examples.