Solve for q q+5/9=1/6

$q + \frac{5}{9} = \frac{1}{6}$

Subtract $\frac{5}{9}$ from both sides of the equation.

$q = \frac{1}{6} - \frac{5}{9}$

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$q = \frac{1}{6} \cdot \frac{3}{3} - \frac{5}{9}$

To write $- \frac{5}{9}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$q = \frac{1}{6} \cdot \frac{3}{3} - \frac{5}{9} \cdot \frac{2}{2}$

Write each expression with a common denominator of $18$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{6}$ by $\frac{3}{3}$ .

$q = \frac{3}{6 \cdot 3} - \frac{5}{9} \cdot \frac{2}{2}$

Multiply $6$ by $3$ .

$q = \frac{3}{18} - \frac{5}{9} \cdot \frac{2}{2}$

Multiply $\frac{5}{9}$ by $\frac{2}{2}$ .

$q = \frac{3}{18} - \frac{5 \cdot 2}{9 \cdot 2}$

Multiply $9$ by $2$ .

$q = \frac{3}{18} - \frac{5 \cdot 2}{18}$

Combine the numerators over the common denominator.

$q = \frac{3 - 5 \cdot 2}{18}$

Simplify the numerator.

Multiply $- 5$ by $2$ .

$q = \frac{3 - 10}{18}$

Subtract $10$ from $3$ .

$q = \frac{- 7}{18}$

Move the negative in front of the fraction.

$q = - \frac{7}{18}$

The result can be shown in multiple forms.

Exact Form:

$q = - \frac{7}{18}$

Decimal Form:

$q = - 0.3\overline{8}$