# Solving One-Step Linear Equations with Mixed Numbers: Addition

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

It is usually easier to do calculations with improper fractions than mixed numbers, but mixed numbers give a better idea of the size of a number. So you should know how to convert back and forth.

To solve an equation that has a mixed number coefficient, we convert the mixed number to an improper fraction as the first step.

Some linear equations can be solved with a single operation. For this type of equation, use the inverse operation to solve. The easiest type involves only an addition or a subtraction.

**
Example :
**

Solve.
*
*

$\frac{3}{4}+p=1\frac{1}{4}$

Rewrite the mixed number as an improper fraction.

$\frac{3}{4}+p=\frac{5}{4}$

The inverse operation of addition is subtraction. Use the subtraction property of equality to subtract $\frac{3}{4}$ from both sides.

$\frac{3}{4}+p-\frac{3}{4}=\frac{5}{4}-\frac{3}{4}$

Simplify.

$p=\frac{2}{4}$

Divide the numerator and the denominator by the GCF, $2$ .

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