Given below are two statements:
Statement I: The product of two rational numbers is always a rational number.
Statement II: The division of two rational numbers is always a rational number.
In the light of the above statements, choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Statement I is true but Statement II is false
A rational number is one that can be written as \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q\ne0\).
Statement I: The product of two rational numbers is always a rational number. True. \(\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}\); here \(ac\) and \(bd\) are integers and \(bd\ne0\), so the product is always rational.
Statement II: The division of two rational numbers is always a rational number. False. Division by zero is not defined, and 0 is a rational number: \(5\div0\) gives no number at all. The quotient is rational only when the divisor is not zero, so “always” makes the statement false.