**What is improper fraction?**

The fraction in which **numerator is greater than denominator** (numerator > denominator) is called improper fraction.

Examples of Improper Fraction

\mathtt{( a) \ \frac{7}{6}}\\\ \\ \mathtt{( b) \ \frac{13}{8}}\\\ \\ \mathtt{( c) \ \frac{11}{7}}\\\ \\ \mathtt{( d) \ \frac{9}{2}}\\\ \\ \mathtt{( e) \ \frac{23}{19}}

**What is Mixed Fraction?**

Mixed fraction is made up of two components:

(a) Whole number

(b) Proper Fraction

Generally the mixed fraction is represented as:

Where;

W is the whole number

A/B is the proper fraction

Examples of Mixed Fractions are:

\mathtt{( a) \ 1\frac{2}{3}}\\\ \\ \mathtt{( b) \ 5\frac{7}{8}}\\\ \\ \mathtt{( c) \ 1\frac{3}{13}}\\\ \\ \mathtt{( d) \ 3\frac{7}{17}}\\\ \\ \mathtt{( e_{\ }) \ 2\frac{3}{9}}

**Convert Improper Fraction into mixed Fraction**

Here we will learn to methods to convert the improper fraction to mixed number.

(a) Division Method

(b) Direct Method

**Division Method to convert improper fraction to mixed fraction**

In this method we use the property that fraction is a form of division.

**For Example:**

Fraction \mathtt{\frac{2}{3}} can be written as 2 ÷ 3

Keeping above property in mind, follow the below steps:

(a) Write the fraction in form of division

(b) Divide the numbers and find quotient and remainder

(c) Write the mixed number as:

Where;

Q = Quotient

R = Remainder

D = Divisor

In just three steps you can convert improper fraction into mixed number.

Let us see some examples for our understanding.

**Example 01**

Convert \mathtt{\frac{4}{3}} into mixed fraction

Follow the below steps:

(a) Write the fraction in form of division

\mathtt{\frac{4}{3}} ⟹ 4 ÷ 3

(b) Divide the numbers

(c) Now do the following arrangement for mixed number

Hence, \mathtt{1\frac{1}{3}} is the required mixed number.

**Example 02**

Convert \mathtt{\frac{17}{8}} into mixed fraction

Follow the below steps:

(a) Represent the fraction into division form

\mathtt{\frac{17}{8}} ⟹ 17 ÷ 8

(b) Divide the numbers

(c) Now do the following arrangement for mixed number

Hence, \mathtt{2\frac{1}{8}} is the required mixed number.

**Example 03**

Convert \mathtt{\frac{29}{5}} into mixed fraction

I have solved this question without showing exact steps.

Hence, \mathtt{5\frac{4}{5}} is the required mixed number.

I hope the method is clear.

Let us understand another method of converting improper fraction into mixed number.

**Direct Method of converting improper fraction to Mixed number**

We can convert improper fraction into mixed number by simple addition calculation.

**For Example**

Convert \mathtt{\frac{5}{4}} into mixed fraction

\mathtt{\Longrightarrow \ \frac{5}{4}}\\\ \\ \mathtt{\Longrightarrow \ \frac{4\ +\ 1}{4} \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{4}{4} \ +\ \frac{1}{4}}\\\ \\ \mathtt{\Longrightarrow \ 1\ +\ \frac{1}{4}}\\\ \\ \mathtt{This\ can\ be\ written\ as:}\\ \\ \mathtt{\Longrightarrow \ 1\frac{1}{4}} \\\ \\

Hence, Mixed fraction of \mathtt{\frac{5}{4}} is \mathtt{ \ 1\frac{1}{4}} \\\ \\

**Example 02**

Convert \mathtt{\frac{11}{7}} into mixed fraction

\mathtt{\frac{11}{7} \ can\ be\ written\ as:}\\\ \\ \mathtt{\Longrightarrow \ \frac{7\ +\ 4}{7} \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{7}{7} \ +\ \frac{4}{7}}\\\ \\ \mathtt{\Longrightarrow \ 1\ +\ \frac{4}{7}}\\\ \\ \mathtt{This\ can\ be\ written\ as:}\\\ \\ \mathtt{\Longrightarrow \ 1\frac{4}{7}} \\\ \\

**Verification of fraction**

In order to check whether the calculated mixed fraction is correct or not, follow the below process.

If \mathtt{A\frac{B}{C}} is the calculated mixed fraction then using below formula will again transform the number into improper fraction.

This will help you verify if the calculation of mixed number is correct or not.

**For Example:**

Find mixed number for \mathtt{\frac{9}{5}} \\\ \\

\mathtt{\frac{9}{5} \ can\ be\ written\ as:}\\\ \\ \mathtt{\Longrightarrow \ \frac{5\ +\ 4}{5} \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{5}{5} \ +\ \frac{4}{5}}\\\ \\ \mathtt{\Longrightarrow \ 1\ +\ \frac{4}{5}}\\\ \\ \mathtt{This\ can\ be\ written\ as:}\\\ \\ \mathtt{\Longrightarrow \ 1\frac{4}{5}}\\\ \\

Check if \mathtt{\ 1\frac{4}{5}} is correct mixed number or not.

In order to do that we will convert the mixed number back to improper fraction using above mentioned formula.

\Longrightarrow \mathtt{\ 1\frac{4}{5}} \\\ \\ \Longrightarrow \ \frac{( 5\times 1) +4}{5}\\\ \\ \Longrightarrow \ \frac{5\ +\ 4}{5}\\\ \\ \Longrightarrow \ \frac{9}{5}

Hence, the solution is correct.

**Improper Fraction to Mixed Number – Solved Problems**

(01) Convert \mathtt{\frac{23}{5}} into mixed fraction.

\mathtt{\frac{23}{5} \ can\ be\ written\ as:}\\\ \\ \mathtt{\Longrightarrow \ \frac{20\ +\ 3}{5} \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{20}{5} \ +\ \frac{3}{5}}\\\ \\ \mathtt{\Longrightarrow \ 4\ +\ \frac{3}{5}}\\\ \\ \mathtt{This\ can\ be\ written\ as:}\\\ \\ \mathtt{\Longrightarrow \ 4\frac{3}{5} \ } \\\ \\

Hence, \mathtt{4\frac{3}{5}} is the required solution.

(02) Convert \mathtt{\frac{29}{4}} into mixed fraction

Hence, \mathtt{7\frac{1}{4}} is the required solution.

(03) Convert \mathtt{\frac{20}{7}} into mixed fraction

\mathtt{\frac{20}{7} \ can\ be\ written\ as:}\\\ \\ \mathtt{\Longrightarrow \ \frac{14\ +\ 6}{7} \ }\\\ \\ \mathtt{\Longrightarrow \ \frac{14}{7} \ +\ \frac{6}{7}}\\\ \\ \mathtt{\Longrightarrow \ 2\ +\ \frac{6}{7}}\\\ \\ \mathtt{This\ can\ be\ written\ as:}\\\ \\ \mathtt{\Longrightarrow \ 2\frac{6}{7} \ }

Hence, \mathtt{2\frac{6}{7}} is the required solution.

(04) Convert \mathtt{\frac{23}{11}} into mixed fraction

Hence, \mathtt{2\frac{1}{11}} is the required solution.