Question

Convert to improper fraction: $3\dfrac{2}{5}$

Answer 1

Hint: Given an improper fraction in the question and we have to convert that improper fraction. A fraction is said to be an improper fraction if the numerator is greater than or equal to the denominator.

Complete step-by-step answer:
We are given with the fraction $3\dfrac{2}{5}$ this fraction is called a mixed fraction because it is a combination of a whole number and a fraction.
Here $3$ in the given fraction is the whole number and $\dfrac{2}{5}$ is the fraction part.
In the fraction part $\dfrac{2}{5}$, the numerator is $2$ and the denominator is $5$.
We have to convert this mixed fraction to an improper fraction;
An improper fraction is a fraction which only has a numerator and a denominator where the numerator is always greater than the denominator.
Now we have to convert the given mixed fraction:
We can write it as $ \Rightarrow 3\dfrac{2}{5}$
The method over here is:
We have to keep the denominator as it is, there will be changes in the numerator only while converting.
Now the numerator has to be changed,
We have to multiply the denominator of the fraction with the whole number and add whatever there is in the numerator, it can be written as:
$ \Rightarrow 3\dfrac{2}{5} = \dfrac{{(5 \times 3) + 2}}{5}$
On simplifying the bracket, we get:
$ \Rightarrow 3\dfrac{2}{5} = \dfrac{{15 + 2}}{5}$
On simplifying the numerator, we get:
$ \Rightarrow 3\dfrac{2}{5} = \dfrac{{17}}{5}$
Therefore, the mixed fraction $3\dfrac{2}{5}$ is equal to the improper fraction $\dfrac{{17}}{5}$.

Hence the correct answer is $\dfrac{{17}}{5}$

Note: In the answer we can see that the numerator is $17$, which is greater than the denominator which is $5$ therefore, it satisfies the condition of being an improper fraction.
There is also a type of fraction called a proper fraction in which the numerator is lesser than the denominator.
For example: $\dfrac{3}{7}$ and $\dfrac{8}{{13}}$.