Question

Example for a proper fraction is: -
A. $\dfrac{28}{13}$
B. \[\dfrac{11}{23}\]
C. \[\dfrac{16}{9}\]
D. \[\dfrac{14}{3}\]

Answer 1

Hint: Before solving this question, we must know about Fraction and Proper Fraction.
FRACTION: A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.
For example, $\dfrac{5}{10}$ is a fraction.
Here, $5$ is a numerator
$10$ is a denominator
PROPER FRACTION: A proper fraction is a type of fraction in which the value of the numerator is smaller than that of the denominator and which given the value that is less than $1$ when we divide the numerator with the denominator. For example: \[\dfrac{15}{27},\dfrac{6}{11},\dfrac{21}{26}\] , etc.

Complete step by step answer:
So, after gaining the knowledge about proper and improper fractions, we will be able to get the answer to this question. We just need to identify the fraction in which the value of the numerator is smaller than that of the denominator.
We will take each option and separate the numerator and denominator and compare them to find whether the fraction is Proper fraction or not.
Let us now solve the question.
A. \[\dfrac{28}{13}\]
In the above fraction numerator$=28$ and denominator$=13$. In this fraction we can say that numerator$>$denominator. So the fraction formed by $28$ as numerator and $13$ as denominator$\left( \dfrac{28}{13} \right)$ is not a Proper Fraction.
Hence, this is not the correct option.
B. \[\dfrac{11}{23}\]
In the above fraction numerator$=11$ and denominator$=23$. In this fraction we can say that numerator$<$denominator. So the fraction formed by $11$ as numerator and $23$ as denominator$\left( \dfrac{23}{11} \right)$ is a Proper Fraction.
Hence, this is the correct option.
C. \[\dfrac{16}{9}\]
In the above fraction numerator$=16$ and denominator$=9$. In this fraction we can say that numerator$>$denominator. So the fraction formed by $16$ as numerator and $9$ as denominator$\left( \dfrac{16}{9} \right)$ is not a Proper Fraction.
Hence, this is not the correct option.
D. \[\dfrac{14}{3}\]
In the above fraction numerator$=14$ and denominator$=3$. In this fraction we can say that numerator$>$denominator. So the fraction formed by $14$ as numerator and $3$ as denominator$\left( \dfrac{14}{3} \right)$ is not a Proper Fraction.
Hence, this is not the correct option.

So, the correct answer is “Option B”.

Note: You can also solve the problem by dividing the numerator with the denominator and obtaining a result. Now compare the results with $1$. If the result is greater than $1$ then that fraction is Improper Fraction. If we get the result is less than $1$ then that fraction is Proper Fraction.
Students often get confused in proper and improper fractions.
Here is the definition of Improper Fractions: -
IMPROPER FRACTION: An improper fraction is a type of fraction in which the value of the numerator is greater than that of the denominator. If you divide the numerator with the denominator the result should be greater than $1$ for Improper fractions. For example: \[\dfrac{27}{15},\dfrac{11}{6},\dfrac{26}{21}\], etc.