### 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 number**and \(4/5\) is a**proper fraction**.**: To convert a mixed fraction to improper fraction, the following steps are to be followed.**

**Converting mixed fraction to improper fraction****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, $3\frac{4}{5}$ \(= 19 / 5\).

**: To convert the improper fraction to mixed fraction, the following steps are to be followed.**

**Converting improper fraction to mixed fraction**

**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, \(15/4 =\) $3\frac{3}{4}$.