Question

The square of a proper fraction is ……… than the given fraction.
$
  A{\text{ smaller}} \\
  {\text{B greater}} \\
  {\text{C equal}} \\
  {\text{D none}} \\
 $

Answer 1

Hint- Here we will proceed by taking an example of proper fraction such that we will do the square of it to get the required result.

Complete step-by-step solution -
Proper fraction – When the numerator is less than the denominator, it is called a proper fraction.
$ \Rightarrow \dfrac{1}{2}$ Where 1 is numerator and 2 is denominator.
As we can see that the numerator is less than the denominator, therefore $\dfrac{1}{2}$is the proper fraction.
Now we will verify the above statement by applying the example of proper fraction i.e. $\dfrac{1}{2}$.
$ \Rightarrow {\left( {\dfrac{1}{2}} \right)^2} = \dfrac{1}{4}$
$ \Rightarrow \left( {\dfrac{1}{4}} \right) < \left( {\dfrac{1}{2}} \right)$
Hence we can see that the square of a proper fraction is lesser than the given fraction.
$\therefore $ option A is right.

Note – In order to solve this type of question, we can assume any example of proper fraction instead of $\dfrac{1}{2}$. Also we must know the difference between proper fraction and improper fraction to solve this type of question.