Question

Which among the following statements is true?

• A. The value of a proper fraction is always larger than the value of its square.
• B. The value of a proper fraction is always smaller than the value of its square.
• C. The value of a proper fraction is always equal to the value of its square.
• D. None of the above

Answer 1

The correct option is A The value of a proper fraction is always larger than the value of its square.

In a proper fraction, the numerator is always less than the denominator. For example, $\frac{2}{5}$, $\frac{3}{7}.$

Therefore, the value of a proper fraction is always lies between $0$ and $1.$

And, the square of a number, which lies between $0$ and $1$ is always less than the number itself.

For an example, take a proper fraction as $\frac{1}{2}=\mathrm{0.5.}$

When we square this proper fraction, we get
$(\frac{1}{2}{)}^2=\frac{1^2}{2^2}=\frac{1}{4}=0.25$

As $0.5>0.25,\frac{1}{2}>(\frac{1}{2}{)}^2$

Therefore, we can say that the value of a proper fraction would always be greater than the value of its square.

$\therefore$ Option (a.) is the correct answer.