# 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.

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

Convert the improper fraction into a mixed number.

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

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

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