Evaluate 2/9+(1/5)÷(1/3)*1/2

$\frac{2}{9} + \frac{1}{5} \div \frac{1}{3} \cdot \frac{1}{2}$

Simplify each term.

To divide by a fraction, multiply by its reciprocal.

$\frac{2}{9} + \frac{1}{5} \cdot 3 \cdot \frac{1}{2}$

Combine $\frac{1}{5}$ and $3$ .

$\frac{2}{9} + \frac{3}{5} \cdot \frac{1}{2}$

Multiply $\frac{3}{5} \cdot \frac{1}{2}$ .

Multiply $\frac{3}{5}$ by $\frac{1}{2}$ .

$\frac{2}{9} + \frac{3}{5 \cdot 2}$

Multiply $5$ by $2$ .

$\frac{2}{9} + \frac{3}{10}$

To write $\frac{2}{9}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{2}{9} \cdot \frac{10}{10} + \frac{3}{10}$

To write $\frac{3}{10}$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$\frac{2}{9} \cdot \frac{10}{10} + \frac{3}{10} \cdot \frac{9}{9}$

Write each expression with a common denominator of $90$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{2}{9}$ by $\frac{10}{10}$ .

$\frac{2 \cdot 10}{9 \cdot 10} + \frac{3}{10} \cdot \frac{9}{9}$

Multiply $9$ by $10$ .

$\frac{2 \cdot 10}{90} + \frac{3}{10} \cdot \frac{9}{9}$

Multiply $\frac{3}{10}$ by $\frac{9}{9}$ .

$\frac{2 \cdot 10}{90} + \frac{3 \cdot 9}{10 \cdot 9}$

Multiply $10$ by $9$ .

$\frac{2 \cdot 10}{90} + \frac{3 \cdot 9}{90}$

Combine the numerators over the common denominator.

$\frac{2 \cdot 10 + 3 \cdot 9}{90}$

Simplify the numerator.

Multiply $2$ by $10$ .

$\frac{20 + 3 \cdot 9}{90}$

Multiply $3$ by $9$ .

$\frac{20 + 27}{90}$

Add $20$ and $27$ .

$\frac{47}{90}$

The result can be shown in multiple forms.

Exact Form:

$\frac{47}{90}$

Decimal Form:

$0.5\overline{2}$