Divide ((2x)/3)÷((3x)/2)

$\frac{2 x}{3} \div \frac{3 x}{2}$

To divide by a fraction, multiply by its reciprocal.

$\frac{2 x}{3} \cdot \frac{2}{3 x}$

Cancel the common factor of $x$ .

Factor $x$ out of $2 x$ .

$\frac{x \cdot 2}{3} \cdot \frac{2}{3 x}$

Factor $x$ out of $3 x$ .

$\frac{x \cdot 2}{3} \cdot \frac{2}{x \cdot 3}$

Cancel the common factor.

$\frac{x \cdot 2}{3} \cdot \frac{2}{x \cdot 3}$

Rewrite the expression.

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

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

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

Multiply $2$ by $2$ .

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

Multiply $3$ by $3$ .

$\frac{4}{9}$

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{9}$

Decimal Form:

$0.\overline{4}$