Question

Which of the following is an improper fraction?
A). $\dfrac{{15}}{1}$
B). $\dfrac{1}{3}$
C). $\dfrac{2}{3}$
D). None of the above

Answer 1

Hint: These basic types of questions can be easily approached by the concept of fraction and improper fraction such as what are the conditions for an improper function, general representation of a fraction number, these instructions can be used to find the improper fraction in the given problem.

Complete step-by-step solution -
We know that the general representation of fraction numbers is $\dfrac{p}{q}$ here p represents numerator and q represents the denominator and $q \ne 0$. The condition for improper fraction says that the numerator of a fraction number should be greater than the denominator. So let’s find out the fraction numbers given in the options satisfies the condition of improper functions
In the first option, $\dfrac{{15}}{1}$ numerator is 15 and denominator is 1 since the numerator is greater than the denominator, therefore, $\dfrac{{15}}{1}$ is an improper fraction
In the second option, $\dfrac{1}{3}$ numerator is 1 and denominator is 3 since the numerator is smaller than the denominator, therefore, $\dfrac{1}{3}$ is not an improper function
In the third option, $\dfrac{2}{3}$ denominator is greater than the numerator, therefore, $\dfrac{2}{3}$ is not an improper function
Since from all the given options, $\dfrac{{15}}{1}$ is the only improper function from all the options
Hence, option A is the correct option.

Note: In the above solution we used the basic concept of fractional numbers which represents the part of a whole-body which is divided into equal parts these concepts can be easily understood by an example suppose if a cake is equally divided into 5 equal parts then the 2 pieces of cake can be represented in fractional form by the help of general fractional numbers formula i.e. $\dfrac{\text{(number of parts)}}{\text{(total numbers of parts)}}$ so the fractional representation of 2 pieces of cakes is $\dfrac{2}{5}$.