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.

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

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.

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