**How to represent the given improper fraction as a mixed number.**

The **main objective** of this question is to represent the given **improper fraction** as a **mixed number**.

This question uses the concept of **improper fractions** and** mixed numbers**. In an improper fraction, the **value** of the **numerator** is always **greater** than the value of the **denominator** or it is **equal** to the **value of the denominator**.

## Expert Answer

We have to represent the **given** **improper fraction** as a **mixed number**.

The **given improper fraction** is:

\[= \space \frac{12}{5}\]

It is an **improper fraction** as the value of the **numerator** is** greater than the value of the denominator**.

We can represent this **improper fraction** as:

\[=\space\frac{10 \space + \space 2}{5} \space \]

**Separating** the term results in:

\[= \space \frac{10}{5} \space + \space \frac{2}{5} \space\]

Now:

\[= \space \frac{10}{5} \space\]

\[= \space 2 \]

Now it can be **written** as:

\[= \space 2 \space + \space \frac{2}{5} \space \]

So,** combining** it will result in:

\[= \space 2 \frac{2}{5} \space \]

Hence, the **mixed number** is $2 \frac{2}{5}$.

## Numeric Answer

The **given improper fraction** $\frac{12}{5 }$ can be represented as the **mixed number** $2\frac{2}{5}$.

## Example

Represent the given improper fractions as mixed numbers.

- \[= \space \frac{22}{5}\]
- \[= \space \frac{32}{5}\]
- \[= \space \frac{42}{5}\]

We have to **represent** the given $3$ **improper fraction** as a **mixed number**.

The first given **improper fraction** is:

\[= \space \frac{22}{5}\]

It is an i**mproper fraction** as the value of the **numerator** is **greater** than the **value of the denominator**.

We can represent this **improper fraction** as:

\[=\space\frac{20 \space + \space 2}{5} \ space \]

**Separating** the term results in:

\[= \space \frac{20}{5} \space + \space \frac{2}{5} \space\]

**Now**:

\[= \space \frac{20}{5} \space\]

\[= \space 4 \]

Now it can be **written** as:

\[= \space 4 \space + \space \frac{2}{5} \space \]

So, **combining** it will result in:

\[= \space 4 \frac{2}{5} \space \]

The second given **improper fraction** is:

\[= \space \frac{32}{5}\]

It is an **improper fraction** as the value of the **numerator** is** greater** than the value of the **denominator**.

We can represent this **improper fraction** as:

\[=\space\frac{30 \space + \space 2}{5} \ space \]

**Separating** the term results in:

\[= \space \frac{30}{5} \space + \space \frac{2}{5} \space\]

**Now**:

\[= \space \frac{30}{5} \space\]

\[= \space 6 \]

**Now** it can be written as:

\[= \space 6 \space + \space \frac{2}{5} \space \]

So, **combining** it will result in:

\[= \space 6 \frac{2}{5} \space \]

The third given **improper fraction** is:

\[= \space \frac{42}{5}\]

It is an **improper fraction** as the value of the numerator is **greater** than the value of the denominator.

We can represent this **improper fraction** as:

\[=\space\frac{40 \space + \space 2}{5} \ space \]

**Separating** the term results in:

\[= \space \frac{40}{5} \space + \space \frac{2}{5} \space\]

**Now**:

\[= \space \frac{40}{5} \space\]

\[= \space 8 \]

Now it can be **written** as:

\[= \space 8 \space + \space \frac{2}{5} \space \]

So, **combining** it will result in:

\[= \space 8 \frac{2}{5} \space \]