Question

$\text{Statement 1:}$ Every fraction is a rational number.
$\text{Statement 2:}$ Every rational number is a fraction.

Which of the following option is correct about the statements given above?

• A. Statement 1 and Statement 2 both are true.
• B. Statement 1 is true and Statement 2 is false.
• C. Statement 1 is false and statement 2 is true.
• D. Statement 1 and statement 2 both are false.

Answer 1

The correct option is B Statement 1 is true and Statement 2 is false.

We know fractions are of the form $\frac{a}{b}$, where $b\ne 0$ and both $a$ and $b$ are whole numbers.

Rational numbers are of the form $\frac{p}{q}$, where $q\ne 0$ and both $p$ and $q$ are integers.

Now, let's take $\frac{2}{3}$ and $\frac{-4}{3}$.
By definition, we can say $\frac{2}{3}$ is fraction and a rational number both but $\frac{-4}{3}$ is a rational number but not a fraction because numerator -4 is not an whole number.

Hence, every fraction is a rational number but every rational number need not to be a fraction.
So, option b is correct.