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.

## Expert Answer

**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:**

\[ 7 \dfrac{ 1 }{ 2 } \]