### Theory:

Mixed fractions contain a whole number and a proper fraction. They can also be represented as an improper fraction.
Example:
$3\frac{4}{5}$; where $$3$$ is a whole numberand $$4/5$$ is a proper fraction.
Converting mixed fraction to improper fraction:
To convert a mixed fraction to improper fraction, the following steps are to be followed.

Step 1: Multiply the denominator of the proper fraction and whole number and add it with the numerator of the fraction to get the numerator of the improper fraction.

Step 2: Denominator of an improper fraction is the same as the denominator of a mixed fraction.
Example:
Convert $3\frac{4}{5}$ to an improper fraction.

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

$$= 5 × 3 = 15 + 4 = 19$$.

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

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

Improper fraction $$= 19 / 5$$.

Thus, $3\frac{4}{5}$ $$= 19 / 5$$.
Converting improper fraction to mixed fraction:
To convert the improper fraction to mixed fraction, the following steps are to be followed.

Divide the given fraction to find quotient and remainder.

The whole number in mixed fraction $$=$$ quotient of division.

The numerator of mixed fraction $$=$$ remainder of a division.

The denominator of mixed fraction $$=$$ denominator of the improper fraction.
Example:
Convert $$15/4$$ to a mixed fraction.

The remainder is $$3$$, the quotient is $$3$$.

The whole number in mixed fraction $$=$$ quotient of division $$= 3$$.

The numerator of mixed fraction $$=$$ reminder of division $$= 3$$.

The denominator of mixed fraction $$=$$ denominator of improper fraction $$= 4$$.

Thus, $$15/4 =$$ $3\frac{3}{4}$.