Home

Solving One-Step Linear Equations with Mixed Numbers: Division

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.

We can solve linear equations when only multiplication or division is involved. If there's a coefficient in front of the variable, multiply by the reciprocal of that number to get a coefficient of 1.

Example:

Solve.

$\frac{x}{6} = 5 \frac{5}{12}$

Rewrite the mixed number as an improper fraction.

$\frac{x}{6} = \frac{65}{12}$

The inverse operation of division is multiplication.

To isolate the variable $x$ (to get a coefficient of $1$ ), multiply both sides by $6$ .

$\frac{x}{6} \times 6 = \frac{65}{12} \times 6$

Cancel the common factors and simplify.

$\begin{array}{l} \frac{x}{\underset{1}{6}} \times \overset{1}{6} = \frac{65}{\underset{2}{12}} \times \overset{1}{6} \\ x = \frac{65}{2} \end{array}$

Convert the improper fraction into a mixed number.

$\frac{65}{2} = 32 \frac{1}{2}$

Therefore, the solution is $32 \frac{1}{2}$ .