Solve for w 2/3+w=1 1/2

$\frac{2}{3} + w = 1 \frac{1}{2}$

Step 1

Simplify the right side.

Convert $1 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$\frac{2}{3} + w = 1 + \frac{1}{2}$

Add $1$ and $\frac{1}{2}$ .

Write $1$ as a fraction with a common denominator.

$\frac{2}{3} + w = \frac{2}{2} + \frac{1}{2}$

Combine the numerators over the common denominator.

$\frac{2}{3} + w = \frac{2 + 1}{2}$

Add $2$ and $1$ .

$\frac{2}{3} + w = \frac{3}{2}$

Step 2

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

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

$w = \frac{3}{2} - \frac{2}{3}$

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

$w = \frac{3}{2} \cdot \frac{3}{3} - \frac{2}{3}$

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

$w = \frac{3}{2} \cdot \frac{3}{3} - \frac{2}{3} \cdot \frac{2}{2}$

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

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

$w = \frac{3 \cdot 3}{2 \cdot 3} - \frac{2}{3} \cdot \frac{2}{2}$

Multiply $2$ by $3$ .

$w = \frac{3 \cdot 3}{6} - \frac{2}{3} \cdot \frac{2}{2}$

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

$w = \frac{3 \cdot 3}{6} - \frac{2 \cdot 2}{3 \cdot 2}$

Multiply $3$ by $2$ .

$w = \frac{3 \cdot 3}{6} - \frac{2 \cdot 2}{6}$

Combine the numerators over the common denominator.

$w = \frac{3 \cdot 3 - 2 \cdot 2}{6}$

Simplify the numerator.

Multiply $3$ by $3$ .

$w = \frac{9 - 2 \cdot 2}{6}$

Multiply $- 2$ by $2$ .

$w = \frac{9 - 4}{6}$

Subtract $4$ from $9$ .

$w = \frac{5}{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$w = \frac{5}{6}$

Decimal Form:

$w = 0.8\overline{3}$