How do you divide rational mixed numbers?

Hint: We are given a statement on how to divide mixed rational numbers and we have to find the method on how to divide mixed rational numbers. Mixed numbers consist of an integer followed by a fraction. It is initially an improper fraction, which then breaks down into a mixed number form. Division of mixed numbers is very similar to the multiplication of mixed numbers. First, transform mixed rational numbers into improper fractions (the ones with numerator greater than denominator). Then perform a division according to general rules of operation on fractions. After this the resulting fraction can be reduced and, if it is improper, transform it into mixed rational numbers.

Complete step by step answer:
Step1:
Given a statement and we have to find the method on how to divide the mixed rational numbers. We will begin by converting each mixed fraction into an improper fraction. Then we will invert or flip upside down the improper fraction that is the divisor. For example we have to divide $30\dfrac{3}{5}$ by $6\dfrac{3}{8}$. The first number produces $30\dfrac{3}{5} = \dfrac{{153}}{5}$ and the second number produces $6\dfrac{3}{8} = \dfrac{{51}}{8}$
$ \Rightarrow \dfrac{{153}}{5} \div \dfrac{{51}}{8}$

Step2:
On converting the division sign into multiplication we will do the reciprocal of the divisor. Then we will reduce the numerator and denominator.
$ \Rightarrow \dfrac{{153}}{5} \times \dfrac{8}{{51}}$
On reducing the term we will get:
$ \Rightarrow \dfrac{3}{5} \times \dfrac{8}{1}$

Step3:
Multiply the first fraction by the second fraction. Multiplication of numerators and denominators are done separately.
$ \Rightarrow \dfrac{{24}}{5}$
Now we will convert the fraction as it is improper into a mixed fraction. On conversion we will get: $4\dfrac{4}{5}$

Note: In these questions when we are given a statement and we have to find out the method. Then it’s easy to simply take a number as an example and solve it in rough work. And the steps that you follow while solving. These are the steps or the methodology that can be followed and you can write those steps as a method for solving these types of questions.