Solve for r 3/8=r+2/3

$\frac{3}{8} = r + \frac{2}{3}$

Rewrite the equation as $r + \frac{2}{3} = \frac{3}{8}$ .

$r + \frac{2}{3} = \frac{3}{8}$

Move all terms not containing $r$ to the right side of the equation.

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

$r = \frac{3}{8} - \frac{2}{3}$

To write $\frac{3}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$r = \frac{3}{8} \cdot \frac{3}{3} - \frac{2}{3}$

To write $- \frac{2}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$r = \frac{3}{8} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{8}{8}$

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{3}{8}$ by $\frac{3}{3}$ .

$r = \frac{3 \cdot 3}{8 \cdot 3} - \frac{2}{3} \cdot \frac{8}{8}$

Multiply $8$ by $3$ .

$r = \frac{3 \cdot 3}{24} - \frac{2}{3} \cdot \frac{8}{8}$

Multiply $\frac{2}{3}$ by $\frac{8}{8}$ .

$r = \frac{3 \cdot 3}{24} - \frac{2 \cdot 8}{3 \cdot 8}$

Multiply $3$ by $8$ .

$r = \frac{3 \cdot 3}{24} - \frac{2 \cdot 8}{24}$

Combine the numerators over the common denominator.

$r = \frac{3 \cdot 3 - 2 \cdot 8}{24}$

Simplify the numerator.

Multiply $3$ by $3$ .

$r = \frac{9 - 2 \cdot 8}{24}$

Multiply $- 2$ by $8$ .

$r = \frac{9 - 16}{24}$

Subtract $16$ from $9$ .

$r = \frac{- 7}{24}$

Move the negative in front of the fraction.

$r = - \frac{7}{24}$

The result can be shown in multiple forms.

Exact Form:

$r = - \frac{7}{24}$

Decimal Form:

$r = - 0.291\overline{6}$