How do you write the given mixed fraction $6\dfrac{3}{5}$ into improper fraction?

Hint: We start solving the problem by recalling the definition of improper fraction as the fraction with the value of numerator is greater than the value of denominator. We then make use of the fact that the conversion of mixed fraction to improper fraction as $a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{c}$. We then make the necessary calculations and check whether the obtained result is improper to complete the solution.

Complete step by step answer:
According to the problem, we are asked to convert the given mixed fraction $6\dfrac{3}{5}$ into improper fraction.
Let us assume $f=6\dfrac{3}{5}$ ---(1).
Let us recall the definition of an improper fraction.
We know that if the value of the numerator is greater than the value of the denominator in a given fraction, then that fraction is known as an improper fraction.
We know that conversion of mixed fraction to improper fraction is $a\dfrac{b}{c}=\dfrac{\left( a\times c \right)+b}{c}$. Let us use this result in equation (1).
$\Rightarrow f=\dfrac{\left( 5\times 6 \right)+3}{5}$.
$\Rightarrow f=\dfrac{30+3}{5}$.
$\Rightarrow f=\dfrac{33}{5}$.
We can see that the value of the numerator is greater than the value of the denominator. So, the obtained answer is an improper fraction.

$\therefore $ We have found the improper fraction form of the given mixed fraction $6\dfrac{3}{5}$ is $\dfrac{33}{5}$.

Note: We should keep in mind that only improper fractions can be written as mixed fractions. We should not write $6\dfrac{3}{5}$ as $\dfrac{63}{5}$ instead of $\dfrac{33}{5}$ which is the common mistake done by students. We should keep in mind that the answer has to be reported in fractions not in decimals, which is also the mistake done by students. Similarly, we can expect problems to find the proper fractions from the given ones: $\dfrac{3}{5}$, $\dfrac{8}{5}$, $\dfrac{1}{2}$, $\dfrac{3}{4}$, $\dfrac{7}{4}$.