Write the Fraction in Simplest Form (2/9)÷(5/12)

$\frac{2}{9} \div \frac{5}{12}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2}{9} \cdot \frac{12}{5}$

Step 2

Cancel the common factor of $3$ .

Factor $3$ out of $9$ .

$\frac{2}{3 (3)} \cdot \frac{12}{5}$

Factor $3$ out of $12$ .

$\frac{2}{3 \cdot 3} \cdot \frac{3 \cdot 4}{5}$

Cancel the common factor.

$\frac{2}{3 \cdot 3} \cdot \frac{3 \cdot 4}{5}$

Rewrite the expression.

$\frac{2}{3} \cdot \frac{4}{5}$

Step 3

Multiply $\frac{2}{3}$ by $\frac{4}{5}$ .

$\frac{2 \cdot 4}{3 \cdot 5}$

Step 4

Multiply $2$ by $4$ .

$\frac{8}{3 \cdot 5}$

Step 5

Multiply $3$ by $5$ .

$\frac{8}{15}$