Simplify ((2a)/(3b))÷((3a)/(2b))

$\frac{2 a}{3 b} \div \frac{3 a}{2 b}$

To divide by a fraction, multiply by its reciprocal.

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

Cancel the common factor of $a$ .

Factor $a$ out of $2 a$ .

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

Factor $a$ out of $3 a$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $b$ .

Factor $b$ out of $3 b$ .

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

Factor $b$ out of $2 b$ .

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

Cancel the common factor.

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

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.

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:

$0.\overline{4}$