# Subtraction: Mixed Numbers

A mixed number is a number expressed as the sum of a whole number and a fraction , such as $3\frac{1}{4}$ .

We can write mixed numbers as improper fractions before adding or subtracting.

## Subtracting Mixed Numbers with Like Denominators

Example:

Subtract.

$5\frac{1}{4}-3\frac{3}{4}$

First, write the mixed numbers as improper fractions.

$\begin{array}{l}5\frac{1}{4}=\frac{21}{4}\\ 3\frac{3}{4}=\frac{15}{4}\end{array}$

Since the denominators are the same, add the numerators.

$\frac{21}{4}-\frac{15}{4}=\frac{6}{4}=\frac{3}{2}$

Write the improper fraction as a mixed number.

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

## Subtracting Mixed Numbers with Unlike Denominators

Example:

Subtract.

$9\frac{3}{4}-5\frac{1}{2}$

First, write the mixed numbers as improper fractions.

$\begin{array}{l}9\frac{3}{4}=\frac{39}{4}\\ 5\frac{1}{2}=\frac{11}{2}\end{array}$

To find the sum, first find the LCD of the fractions.

The LCM of the denominators $4$ and $2$ is $4$ . So, the LCD of the fractions is $4$ .

Rewrite $\frac{11}{2}$ using the LCD.

$\frac{11}{2}=\frac{11}{2}\cdot \frac{2}{2}=\frac{22}{4}$

So,

$\frac{39}{4}-\frac{11}{2}=\frac{39}{4}-\frac{22}{4}$

Since the denominators are the same, add the numerators.

$\frac{39}{4}-\frac{22}{4}=\frac{17}{4}$

Write the improper fraction as a mixed number.

$\frac{17}{4}=4\frac{1}{4}$