Simplify ((2x)/27)÷((4x+20)/9)

$\frac{2 x}{27} \div \frac{4 x + 20}{9}$

To divide by a fraction, multiply by its reciprocal.

$\frac{2 x}{27} \cdot \frac{9}{4 x + 20}$

Simplify terms.

Cancel the common factor of $9$ .

Factor $9$ out of $27$ .

$\frac{2 x}{9 (3)} \cdot \frac{9}{4 x + 20}$

Cancel the common factor.

$\frac{2 x}{9 \cdot 3} \cdot \frac{9}{4 x + 20}$

Rewrite the expression.

$\frac{2 x}{3} \cdot \frac{1}{4 x + 20}$

Multiply $\frac{2 x}{3}$ by $\frac{1}{4 x + 20}$ .

$\frac{2 x}{3 (4 x + 20)}$

Cancel the common factor of $2$ and $4 x + 20$ .

Factor $2$ out of $2 x$ .

$\frac{2 (x)}{3 (4 x + 20)}$

Cancel the common factors.

Factor $2$ out of $3 (4 x + 20)$ .

$\frac{2 (x)}{2 (3 (2 x + 10))}$

Cancel the common factor.

$\frac{2 x}{2 (3 (2 x + 10))}$

Rewrite the expression.

$\frac{x}{3 (2 x + 10)}$

Simplify the denominator.

Factor $2$ out of $2 x + 10$ .

Factor $2$ out of $2 x$ .

$\frac{x}{3 (2 (x) + 10)}$

Factor $2$ out of $10$ .

$\frac{x}{3 (2 x + 2 \cdot 5)}$

Factor $2$ out of $2 x + 2 \cdot 5$ .

$\frac{x}{3 (2 (x + 5))}$

$\frac{x}{3 \cdot 2 (x + 5)}$

Multiply $3$ by $2$ .

$\frac{x}{6 (x + 5)}$