Simplify (x/2)÷((3x^2)/10)

$\frac{x}{2} \div \frac{3 x^{2}}{10}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x}{2} \cdot \frac{10}{3 x^{2}}$

Step 2

Combine.

$\frac{x \cdot 10}{2 (3 x^{2})}$

Step 3

Cancel the common factor of $x$ and $x^{2}$ .

Factor $x$ out of $x \cdot 10$ .

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

Cancel the common factors.

Factor $x$ out of $2 (3 x^{2})$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Cancel the common factor of $10$ and $2$ .

Factor $2$ out of $10$ .

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

Cancel the common factors.

Cancel the common factor.

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

Rewrite the expression.

$\frac{5}{3 x}$