# Addition: 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.

## Adding Mixed Numbers with Like Denominators

**
Example:
**

Add.

$4\frac{3}{4}+2\frac{3}{4}$

First, write the mixed numbers as improper fractions.

$\begin{array}{l}4\frac{3}{4}=\frac{19}{4}\\ 2\frac{3}{4}=\frac{11}{4}\end{array}$

Since the denominators are the same, add the numerators.

$\frac{19}{4}+\frac{11}{4}=\frac{31}{4}$

Write the improper fraction as a mixed number.

$\frac{31}{4}=7\frac{3}{4}$

## Adding Mixed Numbers with Unlike Denominators

**
Example:
**

Add.

$5\frac{1}{4}+1\frac{1}{2}$

First, write the mixed numbers as improper fractions.

$\begin{array}{l}5\frac{1}{4}=\frac{21}{4}\\ 1\frac{1}{2}=\frac{3}{2}\end{array}$

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 $\frac{3}{2}$ using the LCD.

$\frac{3}{2}=\frac{3}{2}\cdot \frac{2}{2}=\frac{6}{4}$

So,

$\frac{21}{4}+\frac{3}{2}=\frac{21}{4}+\frac{6}{4}$

Since the denominators are the same, add the numerators.

$\frac{21}{4}+\frac{6}{4}=\frac{27}{4}$

Write the improper fraction as a mixed number.

$\frac{27}{4}=6\frac{3}{4}$