Question

Example for an improper fraction is
1) \[\dfrac{{25}}{{26}}\]
2) \[\dfrac{{12}}{{13}}\]
3) \[\dfrac{{15}}{{14}}\]
4) \[\dfrac{{19}}{{20}}\]

Answer 1

Hint:
Here we will use the definition of improper function to answer the question. We will analyze each option one by one to check if it is an example of improper function or not.

Complete step by step solution:
We know that improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Suppose there is a fraction \[\dfrac{a}{b}\], if in the fraction \[a\] is greater than or equal to \[b\] then the fraction is called an improper fraction.
Here in the first option, \[\dfrac{{25}}{{26}}\] is given. We can see that 25 is the numerator and 26 is the denominator. As 25 is less than 26 so it is not an example of improper fraction.
Now in the second option, \[\dfrac{{12}}{{13}}\] is given. We can see that 12 is the numerator and 13 is the denominator. Again 12 is less than 13 so it is not an example of improper fraction.
In the third option, \[\dfrac{{15}}{{14}}\] is given. Now we know that 15 is greater than 14 so we can say that the given fraction is an example of improper function.
Now in the last option, \[\dfrac{{19}}{{20}}\] is given. We can see that 19 is the numerator and 20 is the denominator. We know that 19 is less than 20 so it is not an example of improper fraction.
Of all the given options, only \[\dfrac{{15}}{{14}}\] is an example of improper function.

\[\therefore\] Option C is the correct answer.

Note:
We know the definition of three main types of fraction i.e. proper fractions, improper fractions and mixed fractions.
1) Proper fraction is a fraction having the numerator less, or lower in degree, than the denominator.
i.e., Numerator < Denominator
The value of proper fraction after simplification is always less than 1.
2) Improper Fraction is a fraction where the numerator is greater than or equals to the denominator, then it is known as an improper fraction.
i.e., Numerator ≥ Denominator
After the simplification of an improper fraction results in the value which is equal or greater than 1, but not less than 1.
3) Mixed Fraction is the combination of a natural number and fraction. It is basically an improper fraction. After the simplification of a mixed fraction results in the value which is always greater than 1.
An improper fraction can be converted into a mixed fraction.