# 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 $2\frac{1}{7}$

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