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.

Steps

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.

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

Example

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.

Latest Math Topics
Jun 26, 2023
Jun 23, 2023

Math Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Math Worksheets

The math worksheets with answers for your practice with examples.

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.

Learn more

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved