How do you simplify $3\dfrac{1}{2}\div 3$?

Hint: In this question we have a mixed fraction $3\dfrac{1}{2}$ in which the combination of a whole number and a fraction, which we will convert to an improper fraction and then divide that by next term which is $3$ and simplify the expression to get the required solution.

Complete step by step answer:
We have the given expression as $3\dfrac{1}{2}\div 3\to (1)$
Now consider the first term in the expression which is $3\dfrac{1}{2}$
This is a mixed fraction which is a combination of a whole number and a fraction.
The whole number in the mixed fraction is $3$ and the fraction part is $\dfrac{1}{2}$.
Now we can write the mixed fraction as:
$\Rightarrow 3\dfrac{1}{2}$
The method of converting a mixed fraction to improper fraction is that 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:
$\Rightarrow \dfrac{(2\times 3)+1}{2}$
On simplifying the expression, we get:
$\Rightarrow \dfrac{7}{2}$
Now on substituting the value in equation $(1)$, we get:
$\Rightarrow \dfrac{7}{2}\div 3$
Now the expression indicates that we have to divide the fraction by the term $3$.
Since the term is in division, we will take the reciprocal of the term to get it into multiplication.
On taking the reciprocal, we get:
$\Rightarrow \dfrac{7}{2}\times \dfrac{1}{3}$
Now on multiplying the terms, we get:
$\Rightarrow \dfrac{7}{6}$, which is the required solution.

Note: The different types of fractions should be remembered which are a proper fraction in which the numerator is lesser than the denominator, improper fraction in which the numerator is greater than the denominator and mixed fraction which is product of a whole number and a fraction.