### Theory:

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 $\frac{1}{2}\phantom{\rule{0.147em}{0ex}}\mathit{is}\phantom{\rule{0.147em}{0ex}}\frac{2}{1}$. 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, $\frac{1}{2}\phantom{\rule{0.147em}{0ex}}\mathit{and}\phantom{\rule{0.147em}{0ex}}\frac{2}{1}$ are reciprocals of each other.
Example:
$\begin{array}{l}\frac{\frac{-1}{2}}{\frac{5}{6}}=?\\ \\ \mathit{Step}\phantom{\rule{0.147em}{0ex}}\mathit{1}:\mathit{Take}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{reciprocal}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\mathit{divisor}\phantom{\rule{0.147em}{0ex}}\left(\frac{5}{6}\right)\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\frac{6}{5}\\ \\ \mathit{Step}\phantom{\rule{0.147em}{0ex}}\mathit{2}:\mathit{Multiply}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{dividend}\phantom{\rule{0.147em}{0ex}}\left(\frac{-1}{2}\right)\phantom{\rule{0.147em}{0ex}}\mathit{by}\phantom{\rule{0.147em}{0ex}}\frac{6}{5}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\frac{-1}{2}×\frac{6}{5}\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\frac{-3}{5}\\ \\ \frac{\mathit{New}\phantom{\rule{0.147em}{0ex}}\mathit{numerator}}{\mathit{New}\phantom{\rule{0.147em}{0ex}}\mathit{denominator}}=\frac{-3}{5}\end{array}$
 Number of negative fractions Sign of new fraction Even $$+$$ Odd $$-$$

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:
$\begin{array}{l}\mathit{Let}\phantom{\rule{0.147em}{0ex}}\mathit{us}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\mathit{find}\phantom{\rule{0.147em}{0ex}}1÷\frac{1}{4}\\ \mathit{Step}\phantom{\rule{0.147em}{0ex}}\mathit{1}:\mathit{Reciprocal}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{divisor},\frac{1}{4} \mathit{is}\phantom{\rule{0.147em}{0ex}}\frac{4}{1}\\ \mathit{Step}\phantom{\rule{0.147em}{0ex}}2:\mathit{Multiply}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{dividend}\phantom{\rule{0.147em}{0ex}}\left(1\right)\phantom{\rule{0.147em}{0ex}}\mathit{by}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}\frac{4}{1}=1×4=4\end{array}$
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:
$\begin{array}{l}\mathit{Let}\phantom{\rule{0.147em}{0ex}}\mathit{us}\phantom{\rule{0.147em}{0ex}}\mathit{find}\phantom{\rule{0.147em}{0ex}}\frac{1}{4}÷1\\ \mathit{Step}\phantom{\rule{0.147em}{0ex}}\mathit{1}:\mathit{Reciprocal}\phantom{\rule{0.147em}{0ex}}\mathit{of}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{divisor},\mathit{1}\phantom{\rule{0.147em}{0ex}}\mathit{is}\phantom{\rule{0.147em}{0ex}}1\\ \mathit{Step}\phantom{\rule{0.147em}{0ex}}2:\mathit{Multiply}\phantom{\rule{0.147em}{0ex}}\mathit{the}\phantom{\rule{0.147em}{0ex}}\mathit{dividend}\phantom{\rule{0.147em}{0ex}}\frac{1}{4}\phantom{\rule{0.147em}{0ex}}\mathit{by}\phantom{\rule{0.147em}{0ex}}\phantom{\rule{0.147em}{0ex}}1=\frac{1}{4}\end{array}$
Division of mixed fractions:

First, convert the mixed fractions to improper fractions and divide the fractions.