Solve for r r+2/3=5/6

$r + \frac{2}{3} = \frac{5}{6}$

Subtract $\frac{2}{3}$ from both sides of the equation.

$r = \frac{5}{6} - \frac{2}{3}$

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{3}$ by $\frac{2}{2}$ .

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

Multiply $3$ by $2$ .

$r = \frac{5}{6} - \frac{2 \cdot 2}{6}$

Combine the numerators over the common denominator.

$r = \frac{5 - 2 \cdot 2}{6}$

Simplify the numerator.

Multiply $- 2$ by $2$ .

$r = \frac{5 - 4}{6}$

Subtract $4$ from $5$ .

$r = \frac{1}{6}$

The result can be shown in multiple forms.

Exact Form:

$r = \frac{1}{6}$

Decimal Form:

$r = 0.1\overline{6}$