Math Doubts

Mixed fractions

A mixer of a whole quantity and a fraction is called a mixed fraction.


A mixed fraction is basically a fraction but it consists of two parts, which are an integer part and a proper fraction part. You may wonder by seeing the numbers in the following special form.

$1\dfrac{3}{4}, 2\dfrac{1}{6}, -5\dfrac{5}{8}, \ldots$

The all of them are representing mixed fractions numerically.

In mathematics, the mixed fractions are formed by the mixer of a proper fraction with one or more whole quantities. If a proper fraction is added to a whole quantity, then the quantity becomes a fraction. Hence, the fractions are called as the mixed fractions.

Remember, the quantity of a mixed fraction is always greater than one. So, they are basically improper fractions but all improper fractions are not mixed fractions.


Let us understand the concept of mixed fractions from the following examples.

Example – 1

Consider two circles and divide a circle into three equal parts. Now, take a circle and two parts from the three parts of another circle as a fraction.

mixed fraction

Due to mixing a fraction with a whole quantity, a mixed fraction is formed and it can be calculated mathematically.

  1. The quantity of a full circle is $1$.
  2. The quantity of the fraction of another circle is $\large \frac{2}{3}$.

The sum of the quantities is equal to the mixed fraction.

$\implies$ Mixed fraction $\,=\,$ $1+\dfrac{2}{3}$

It is simply expressed in the following special form in mathematics.

$\,\,\, \therefore \,\,\,\,\,\,$ Mixed fraction $\,=\,$ $1\dfrac{2}{3}$

Example – 2

Take four rectangles but split a rectangle as five equal parts. Now, take three rectangles and three parts from five parts of another rectangle as a fraction.

mixed fraction

Their mixer forms a mixed fraction, which can be evaluated mathematically.

  1. The quantity of whole rectangles is $3$.
  2. The quantity of the fraction of remaining rectangle is $\large \frac{3}{5}$.

Let’s calculate the mixed fraction.

$\implies$ Mixed fraction $\,=\,$ $3+\dfrac{3}{5}$

$\,\,\, \therefore \,\,\,\,\,\,$ Mixed fraction $\,=\,$ $3\dfrac{3}{5}$

Thus, the mixed fractions are formed geometrically and also above steps are used to calculate them mathematically.

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