Solving One-Step Linear Equations with Mixed Numbers: Subtraction

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.

$x - 3 \frac{1}{2} = \frac{17}{2}$

Rewrite the mixed number as an improper fraction.

$x - \frac{7}{2} = \frac{17}{2}$

The inverse operation of subtraction is addition. Use the addition property of equality to add $\frac{7}{2}$ to both sides.

$x - \frac{7}{2} + \frac{7}{2} = \frac{17}{2} + \frac{7}{2}$

Simplify.

$x = \frac{24}{2}$

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

$x = 12$

Solving One-Step Linear Equations with Mixed Numbers: Subtraction

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