A mixed fraction is basically an improper fraction but it is expressed in a special form for representing an integer part and a proper fraction at a time.

$Mixed \, fraction$ $\,=\,$ $(Integer \, part) \, \dfrac{Numerator}{Denominator}$

In some cases, a mixed fraction should be converted into an improper fraction. So, it is essential to learn how to change a mixed a fraction into an improper fraction mathematically.

There are three simple steps to change any mixed fraction as an improper fraction.

- Multiply the Integer part by the denominator of the fraction.
- Add the product to the numerator of the proper fraction.
- Display the sum as numerator with same denominator.

The three steps can be written as a formula, which helps us to change any mixed fraction as an improper fraction.

$Improper \, fraction$ $\,=\,$ $\dfrac{(Integer \, part) \times Denominator + Numerator}{Denominator}$

Convert the mixed fraction $7\dfrac{2}{5}$ as an improper fraction.

In this example, $7$ is an integer, $2$ is a numerator and $5$ is a denominator. Multiply the integer $7$ by the denominator $5$ and then add the product to the numerator $2$. The sum of them is written as numerator of the improper fraction but its denominator is same as the denominator of the fraction in the mixed fraction.

$Improper \, fraction$ $\,=\,$ $\dfrac{(7 \times 5)+2}{5}$

$\implies$ $Improper \, fraction$ $\,=\,$ $\dfrac{35+2}{5}$

$\,\,\, \therefore \,\,\,\,\,\,$ $Improper \, fraction$ $\,=\,$ $\dfrac{37}{5}$

Therefore, the mixed fraction $7\dfrac{2}{5}$ is converted as an improper fraction $\dfrac{37}{5}$ mathematically.

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