# Writing an improper fraction as a mixed number

An **improper fraction** is a fraction where the numerator is greater than the denominator.

A **mixed number** is a number that consists of a **whole number** and **proper fraction**. For example, $1\frac{1}{2}$ is a mixed number.

**Rules to write an improper fraction as a mixed number**

To write an improper fraction as a

**mixed number**, we rewrite it as a division problem and divide.On dividing the numerator by the denominator, we get a quotient which is a whole number and a remainder which is written as a proper fraction.

The whole number and the proper fraction together is the mixed number.

*So, an improper fraction can always be written as a mixed number.*

Write $\frac{3}{2}$ as a mixed number

### Solution

**Step 1:**

$\frac{3}{2}$ is an improper fraction as the numerator 3 is greater than 2, the denominator.

**Step 2:**

By dividing 3 by 2 we get whole number 1 as quotient and 1 as remainder which is written as proper fraction $\frac{1}{2}$.

**Step 3:**

So, $\frac{3}{2} = 1\frac{1}{2}$

Write the improper fraction $\frac{11}{4}$ as a mixed number.

### Solution

**Step 1:**

$\frac{11}{4}$ is an improper fraction as numerator 11 is greater than 4, the denominator.

**Step 2:**

We divide 11 by 4, and get 2 as a quotient and 3 as a remainder which is written as proper fraction $\frac{3}{4}$.

**Step 3:**

So, $\frac{11}{4}$ can be written as a mixed number $2\frac{3}{4}$

$\frac{11}{4} = 2\frac{3}{4}$

Write the improper fraction as a mixed number.

$\frac{15}{7}$

### Solution

**Step 1:**

$\frac{15}{7}$ is an improper fraction as numerator 15 is greater than the denominator 7.

**Step 2:**

We divide 15 by 7, and get 2 as a quotient and 1 as a remainder which is written as a proper fraction $\frac{1}{7}$.

**Step 3:**

So, $\frac{15}{7}$ can be written as a mixed number $2\frac{1}{7}$

$\frac{15}{7} = 2\frac{1}{7}$