# Improper Fraction to Mixed Number

Improper fractions are converted to mixed numbers to make them easier to understand and visualize. It also helps simplify comparisons and calculations and provides a clearer representation of the value.

It is important to note that an improper fraction and its corresponding mixed number have the same value. They are only represented differently.

## How To Convert

To convert an improper fraction ${\dfrac{7}{5}}$ to a mixed number, we follow the following steps.

Step 1: Dividing the Numerator by the Denominator

7 ÷ 5

The quotient = 1 and the remainder = 2.

Step 2: Writing in the Form ${Quotient\dfrac{Remainder}{Divisor}}$

The mixed number obtained is ​${1\dfrac{2}{5}}$

Let us consider another example.

To convert ${\dfrac{37}{6}}$ into a mixed number, we divide 37 by 6

37 ÷ 6

The quotient = 6 and the remainder = 1

Thus, the improper fraction ${\dfrac{37}{6}}$ as a mixed number is ${6\dfrac{1}{6}}$

## Adding Improper Fraction to Mixed Number

Let us add ${\dfrac{8}{3}}$ and ${1\dfrac{3}{4}}$

Converting the Mixed Number to an Improper Fraction

${1\dfrac{3}{4}}$ = ${\dfrac{\left( 1\times 4\right) +3}{4}}$ = ${\dfrac{7}{4}}$

Now, ${\dfrac{8}{3}+1\dfrac{3}{4}}$

= ${\dfrac{8}{3}+\dfrac{7}{4}}$

= ${\dfrac{8\times 4}{3\times 4}+\dfrac{7\times 3}{4\times 3}}$

= ${\dfrac{32}{12}+\dfrac{21}{12}}$

=  ${\dfrac{32+21}{12}}$

= ${\dfrac{53}{12}}$

Converting the Result to a Mixed Number

= ${4\dfrac{5}{12}}$

Thus, the sum is ${4\dfrac{5}{12}}$

## Solved Examples

Convert the improper fraction ${\dfrac{8}{3}}$ to mixed number.

Solution:

Here,
The numerator = 8
The denominator = 3
8 ÷ 3
The quotient = 2 and the remainder = 2
Thus, the improper fraction ${\dfrac{8}{3}}$ as a mixed number is ${2\dfrac{2}{3}}$

E.g.2. Change the improper fraction ${\dfrac{9}{4}}$ to mixed number.

Solution:

Here,
The numerator = 9
The denominator = 4
9 ÷ 4
The quotient = 2 and the remainder = 1
Thus, the improper fraction ${\dfrac{9}{4}}$ as a mixed number is ${2\dfrac{1}{4}}$

Turn the improper fraction ${\dfrac{62}{13}}$ into mixed number.

Solution:

Here,
The numerator = 62
The denominator = 13
62 ÷ 13
The quotient = 4 and the remainder = 10
Thus, the mixed number is ${4\dfrac{10}{13}}$

E.g.4.

Write the improper fraction ${\dfrac{18}{7}}$ as mixed number.

Solution:

Here,
The numerator = 18
The denominator = 7
18 ÷ 7
The quotient = 2 and the remainder = 4
Thus, the mixed number is ${2\dfrac{4}{7}}$

Add the improper fraction and the mixed number:
${\dfrac{7}{5}}$ and ${1\dfrac{2}{3}}$

Solution:

Here,
${1\dfrac{2}{3}}$ = ${\dfrac{\left( 1\times 3\right) +2}{3}}$ = ${\dfrac{5}{3}}$
Now, ${\dfrac{7}{5}+1\dfrac{2}{3}}$
= ${\dfrac{7}{5}+\dfrac{5}{3}}$
= ${\dfrac{7\times 3}{5\times 3}+\dfrac{5\times 5}{3\times 5}}$
= ${\dfrac{21}{15}+\dfrac{25}{15}}$
=  ${\dfrac{21+25}{15}}$
= ${\dfrac{46}{15}}$
= ${3\dfrac{1}{15}}$
Thus, the sum is ${3\dfrac{1}{15}}$