Pre-Algebra Examples

$\frac{2 p r \cdot r}{4} - \frac{r \cdot r}{2}$

Step 1

Simplify each term.

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Step 1.1

Multiply $r$ by $r$ by adding the exponents.

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Step 1.1.1

Move $r$ .

$\frac{2 p (r \cdot r)}{4} - \frac{r \cdot r}{2}$

Step 1.1.2

Multiply $r$ by $r$ .

$\frac{2 p r^{2}}{4} - \frac{r \cdot r}{2}$

Step 1.2

Cancel the common factor of $2$ and $4$ .

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Step 1.2.1

Factor $2$ out of $2 p r^{2}$ .

$\frac{2 (p r^{2})}{4} - \frac{r \cdot r}{2}$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $2$ out of $4$ .

$\frac{2 (p r^{2})}{2 \cdot 2} - \frac{r \cdot r}{2}$

Step 1.2.2.2

Cancel the common factor.

$\frac{2 (p r^{2})}{2 \cdot 2} - \frac{r \cdot r}{2}$

Step 1.2.2.3

Rewrite the expression.

$\frac{p r^{2}}{2} - \frac{r \cdot r}{2}$

Step 1.3

Multiply $r$ by $r$ .

$\frac{p r^{2}}{2} - \frac{r^{2}}{2}$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{p r^{2} - r^{2}}{2}$

Step 2.2

Factor $r^{2}$ out of $p r^{2} - r^{2}$ .

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Step 2.2.1

Factor $r^{2}$ out of $p r^{2}$ .

$\frac{r^{2} p - r^{2}}{2}$

Step 2.2.2

Factor $r^{2}$ out of $- r^{2}$ .

$\frac{r^{2} p + r^{2} \cdot - 1}{2}$

Step 2.2.3

Factor $r^{2}$ out of $r^{2} p + r^{2} \cdot - 1$ .

$\frac{r^{2} (p - 1)}{2}$