### Theory:

1. Dividing a fraction by another fraction:
To divide a fractional number with another fractional number, follow the steps below:

Step 1: Take the reciprocal of the divisor.

Step 2: Multiply the reciprocal of the divisor with the dividend to get the new numerator and denominator of the fraction.

Reciprocal of a fraction: The reciprocal of a fraction can be obtained by interchanging the numerator and denominator of the fraction. For example, reciprocal of $\frac{1}{2}$ is $\frac{2}{1}$ The non-zero numbers whose product with each other is $$1$$ are called the reciprocals of each other that is, $\frac{1}{2}\phantom{\rule{0.147em}{0ex}}×\frac{2}{1}=1\phantom{\rule{0.147em}{0ex}}$. Hence, $\frac{1}{2}$ and $\frac{2}{1}$ are reciprocals of each other.

Let us find the value of $\frac{\frac{1}{2}}{\frac{5}{6}}=?$

Step 1: Take the reciprocal of divisor $\left(\frac{5}{6}\right)\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\frac{6}{5}$.

Step 2: Multiply the dividend $\left(\frac{1}{2}\right)$ by $\frac{6}{5}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\frac{1}{2}×\frac{6}{5}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\frac{3}{5}$

$$\frac{\text{New Numerator}}{\text{New Denominator}}$$ $$=$$ $\frac{3}{5}$
2. Division of the whole number by a fraction:
Dividing a whole number by a fraction will follow the same procedure as dividing a fraction by another fraction.
Example:
Let us find $\phantom{\rule{0.147em}{0ex}}1÷\frac{1}{4}$
Step 1: Reciprocal of the divisor, $\frac{1}{4}$ is $\frac{4}{1}$
Step 2: Multiply the dividend ($$1$$) by $\frac{4}{1}=1×4=4$.
3. Division of a fraction by a whole number:
Dividing a fractional number by a whole number will follow the same procedure as dividing a fraction by another fraction.
Example:
Let us find $\frac{1}{4}÷1$.

Step 1: Reciprocal of the divisor, $$1$$ is $$1$$.

Step 2: Multiply the dividend $\frac{1}{4}$ by $1=\frac{1}{4}$.
4. Division of mixed fractions:
First, convert the mixed fractions to improper fractions and divide the fractions.
Example:
Convert $4\frac{10}{5}$ to an improper fraction.

Step 1: Numerator of improper fraction $$=$$ (denominator of the proper fraction $$×$$ whole number) $$+$$ numerator of a proper fraction.

$$= 5 × 4 = 20 + 10 = 30$$.

Step 2: Denominator of improper fraction $$=$$ denominator of the mixed fraction.

The denominator of improper fraction $$= 5$$.

Improper fraction $$= 30 / 5 = 6$$.

Thus,  $4\frac{10}{5}$ $$= 6$$.