# What is 12/5 as a mixed fraction?

The aim of this question is to learn how to convert simple fractions into mixed fractions.

Fractions can be subdivided into two types, proper and improper. A fraction is said to be a proper fraction if the numerator magnitude is smaller than the denominator magnitude. $\dfrac{ 1 }{ 2 }$ is an example of a proper fraction.

An improper fraction is such a fraction whose numerator value is equal to or greater than that of the denominator. Improper fractions can be converted into mixed fractions. $\dfrac{ 88 }{ 2 }$ is an example of a proper fraction.

A mixed fraction is a type of fraction that has a whole number part and a proper fraction part. $14 \ + \ \dfrac{ 1 }{ 2 }$ is an example of a proper fraction.

Given the fraction:

$\dfrac{ 12 }{ 5 }$

Substituting $12 \ = \ 10 \ + \ 2$ in the above equation:

$\dfrac{ 10 \ + \ 2 }{ 5 }$

Separating the denominator:

$\dfrac{ 10 }{ 5 } \ + \ \dfrac{ 2 }{ 5 }$

Substituting $10 \ = \ ( 2 )( 5 )$ in the above equation:

$\dfrac{ ( 2 )( 5 ) }{ 5 } \ + \ \dfrac{ 2 }{ 5 }$

$2 \times \dfrac{ 5 }{ 5 } \ + \ \dfrac{ 2 }{ 5 }$

$2 \times 1 \ + \ \dfrac{ 2 }{ 5 }$

$2 \ + \ \dfrac{ 2 }{ 5 }$

Which can be written as:

$2 \dfrac{ 2 }{ 5 }$

## Numerical Results

$2 \dfrac{ 2 }{ 5 }$

## Example

Write the mixed fraction of 33/8 and 15/2.

Part (a) – Given the fraction:

$\dfrac{ 33 }{ 8 }$

Substituting $33 \ = \ 32 \ + \ 1$ in the above equation:

$\dfrac{ 32 \ + \ 1 }{ 8 }$

Separating the denominator:

$\dfrac{ 32 }{ 8 } \ + \ \dfrac{ 1 }{ 8 }$

Substituting $32 \ = \ ( 4 )( 8 )$ in the above equation:

$\dfrac{ ( 4 )( 8 ) }{ 8 } \ + \ \dfrac{ 1 }{ 8 }$

$4 \ + \ \dfrac{ 1 }{ 8 }$

Which can be written as:

$4 \dfrac{ 1 }{ 8 }$

Part (b) – Given the fraction:

$\dfrac{ 15 }{ 2 }$

Substituting $15 \ = \ 14 \ + \ 1$ in the above equation:

$\dfrac{ 14 \ + \ 1 }{ 2 }$

Separating the denominator:

$\dfrac{ 14 }{ 2 } \ + \ \dfrac{ 1 }{ 2 }$

Substituting $14 \ = \ ( 7 )( 2 )$ in the above equation:

$\dfrac{ ( 7 )( 2 ) }{ 2 } \ + \ \dfrac{ 1 }{ 2 }$

$7 \ + \ \dfrac{ 1 }{ 2 }$

Which can be written as:

$7 \dfrac{ 1 }{ 2 }$