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.

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

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.

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