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Solving One-Step Linear Equations with Mixed Numbers: Multiplication

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.

$1 \frac{1}{4} x = 1 \frac{1}{9}$

Rewrite the mixed numbers as improper fractions.

$\frac{5}{4} x = \frac{10}{9}$

The inverse operation of division is multiplication.

To isolate the variable $x$ (to get a coefficient of $1$ ), multiply both sides by $\frac{4}{5}$ which is the reciprocal of $\frac{5}{4}$ .

$\frac{4}{5} \cdot (\frac{5}{4} x) = \frac{10}{9} \cdot \frac{4}{5}$

Simplify.

$\frac{4}{5} \cdot (\frac{5}{4} x) = \frac{{}^{2}10}{9} \cdot \frac{4}{5_{1}}$

$x = \frac{8}{9}$

Therefore, the solution is $\frac{8}{9}$ .