Evaluate 1/2+(1/3)÷(1/2-1/3)

$\frac{1}{2} + \frac{1}{3} \div (\frac{1}{2} - \frac{1}{3})$

Simplify each term.

Rewrite the division as a fraction.

$\frac{1}{2} + \frac{\frac{1}{3}}{\frac{1}{2} - \frac{1}{3}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2} + \frac{1}{3} \cdot \frac{1}{\frac{1}{2} - \frac{1}{3}}$

Simplify the denominator.

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{2} + \frac{1}{3} \cdot \frac{1}{\frac{1}{2} \cdot \frac{3}{3} - \frac{1}{3}}$

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{2} + \frac{1}{3} \cdot \frac{1}{\frac{1}{2} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{2}{2}}$

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

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{1}{2} + \frac{1}{3} \cdot \frac{1}{\frac{3}{2 \cdot 3} - \frac{1}{3} \cdot \frac{2}{2}}$

Multiply $2$ by $3$ .

$\frac{1}{2} + \frac{1}{3} \cdot \frac{1}{\frac{3}{6} - \frac{1}{3} \cdot \frac{2}{2}}$

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$\frac{1}{2} + \frac{1}{3} \cdot \frac{1}{\frac{3}{6} - \frac{2}{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{1}{2} + \frac{1}{3} \cdot \frac{1}{\frac{3}{6} - \frac{2}{6}}$

Combine the numerators over the common denominator.

$\frac{1}{2} + \frac{1}{3} \cdot \frac{1}{\frac{3 - 2}{6}}$

Subtract $2$ from $3$ .

$\frac{1}{2} + \frac{1}{3} \cdot \frac{1}{\frac{1}{6}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{1}{2} + \frac{1}{3} (1 \cdot 6)$

Multiply $6$ by $1$ .

$\frac{1}{2} + \frac{1}{3} \cdot 6$

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

$\frac{1}{2} + \frac{1}{3} \cdot (3 (2))$

Cancel the common factor.

$\frac{1}{2} + \frac{1}{3} \cdot (3 \cdot 2)$

Rewrite the expression.

$\frac{1}{2} + 2$

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

$\frac{1}{2} + 2 \cdot \frac{2}{2}$

Combine $2$ and $\frac{2}{2}$ .

$\frac{1}{2} + \frac{2 \cdot 2}{2}$

Combine the numerators over the common denominator.

$\frac{1 + 2 \cdot 2}{2}$

Simplify the numerator.

Multiply $2$ by $2$ .

$\frac{1 + 4}{2}$

Add $1$ and $4$ .

$\frac{5}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$

Evaluate 1/2+(1/3)÷(1/2-1/3)

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