Solve for n 7/9=n+2/3

$\frac{7}{9} = n + \frac{2}{3}$

Step 1

Rewrite the equation as $n + \frac{2}{3} = \frac{7}{9}$ .

$n + \frac{2}{3} = \frac{7}{9}$

Step 2

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

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

$n = \frac{7}{9} - \frac{2}{3}$

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

$n = \frac{7}{9} - \frac{2}{3} \cdot \frac{3}{3}$

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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

$n = \frac{7}{9} - \frac{2 \cdot 3}{3 \cdot 3}$

Multiply $3$ by $3$ .

$n = \frac{7}{9} - \frac{2 \cdot 3}{9}$

Combine the numerators over the common denominator.

$n = \frac{7 - 2 \cdot 3}{9}$

Simplify the numerator.

Multiply $- 2$ by $3$ .

$n = \frac{7 - 6}{9}$

Subtract $6$ from $7$ .

$n = \frac{1}{9}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$n = \frac{1}{9}$

Decimal Form:

$n = 0.\overline{1}$