Pre-Algebra Examples

$\frac{2 x^{2}}{5} \div \frac{x^{3}}{15}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 x^{2}}{5} \cdot \frac{15}{x^{3}}$

Step 2

Combine.

$\frac{2 x^{2} \cdot 15}{5 x^{3}}$

Step 3

Cancel the common factor of $x^{2}$ and $x^{3}$ .

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Step 3.1

Factor $x^{2}$ out of $2 x^{2} \cdot 15$ .

$\frac{x^{2} (2 \cdot 15)}{5 x^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x^{2}$ out of $5 x^{3}$ .

$\frac{x^{2} (2 \cdot 15)}{x^{2} (5 x)}$

Step 3.2.2

Cancel the common factor.

$\frac{x^{2} (2 \cdot 15)}{x^{2} (5 x)}$

Step 3.2.3

Rewrite the expression.

$\frac{2 \cdot 15}{5 x}$

$\frac{2 \cdot 15}{5 x}$

$\frac{2 \cdot 15}{5 x}$

Step 4

Cancel the common factor of $15$ and $5$ .

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Step 4.1

Factor $5$ out of $2 \cdot 15$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $5$ out of $5 x$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

Multiply $2$ by $3$ .

$\frac{6}{x}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$