Evaluate 2/3*1/3+(1/2)÷(2/3)

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

Simplify each term.

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

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

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

Multiply $3$ by $3$ .

$\frac{2}{9} + \frac{1}{2} \div \frac{2}{3}$

To divide by a fraction, multiply by its reciprocal.

$\frac{2}{9} + \frac{1}{2} \cdot \frac{3}{2}$

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

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

$\frac{2}{9} + \frac{3}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{2}{9} + \frac{3}{4}$

To write $\frac{2}{9}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{2}{9} \cdot \frac{4}{4} + \frac{3}{4}$

To write $\frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{2}{9} \cdot \frac{4}{4} + \frac{3}{4} \cdot \frac{9}{9}$

Write each expression with a common denominator of $36$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{9}$ by $\frac{4}{4}$ .

$\frac{2 \cdot 4}{9 \cdot 4} + \frac{3}{4} \cdot \frac{9}{9}$

Multiply $9$ by $4$ .

$\frac{2 \cdot 4}{36} + \frac{3}{4} \cdot \frac{9}{9}$

Multiply $\frac{3}{4}$ by $\frac{9}{9}$ .

$\frac{2 \cdot 4}{36} + \frac{3 \cdot 9}{4 \cdot 9}$

Multiply $4$ by $9$ .

$\frac{2 \cdot 4}{36} + \frac{3 \cdot 9}{36}$

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 + 3 \cdot 9}{36}$

Simplify the numerator.

Multiply $2$ by $4$ .

$\frac{8 + 3 \cdot 9}{36}$

Multiply $3$ by $9$ .

$\frac{8 + 27}{36}$

Add $8$ and $27$ .

$\frac{35}{36}$

The result can be shown in multiple forms.

Exact Form:

$\frac{35}{36}$

Decimal Form:

$0.97\overline{2}$