Math Doubts

Converting the Mixed fractions into Improper fractions

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.

  1. Multiply the Integer part by the denominator of the fraction.
  2. Add the product to the numerator of the proper fraction.
  3. 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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