Pre-Algebra Examples

$\frac{p^{3} q}{r} \div \frac{p q^{4}}{r^{5}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{p^{3} q}{r} \cdot \frac{r^{5}}{p q^{4}}$

Step 2

Combine.

$\frac{p^{3} q r^{5}}{r (p q^{4})}$

Step 3

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

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Step 3.1

Factor $p$ out of $p^{3} q r^{5}$ .

$\frac{p (p^{2} q r^{5})}{r (p q^{4})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $p$ out of $r (p q^{4})$ .

$\frac{p (p^{2} q r^{5})}{p (r (q^{4}))}$

Step 3.2.2

Cancel the common factor.

$\frac{p (p^{2} q r^{5})}{p (r (q^{4}))}$

Step 3.2.3

Rewrite the expression.

$\frac{p^{2} q r^{5}}{r (q^{4})}$

$\frac{p^{2} q r^{5}}{r (q^{4})}$

$\frac{p^{2} q r^{5}}{r (q^{4})}$

Step 4

Cancel the common factor of $q$ and $q^{4}$ .

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Step 4.1

Factor $q$ out of $p^{2} q r^{5}$ .

$\frac{q (p^{2} r^{5})}{r (q^{4})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $q$ out of $r (q^{4})$ .

$\frac{q (p^{2} r^{5})}{q (r (q^{3}))}$

Step 4.2.2

Cancel the common factor.

$\frac{q (p^{2} r^{5})}{q (r (q^{3}))}$

Step 4.2.3

Rewrite the expression.

$\frac{p^{2} r^{5}}{r (q^{3})}$

$\frac{p^{2} r^{5}}{r (q^{3})}$

$\frac{p^{2} r^{5}}{r (q^{3})}$

Step 5

Cancel the common factor of $r^{5}$ and $r$ .

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Step 5.1

Factor $r$ out of $p^{2} r^{5}$ .

$\frac{r (p^{2} r^{4})}{r (q^{3})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Cancel the common factor.

$\frac{r (p^{2} r^{4})}{r q^{3}}$

Step 5.2.2

Rewrite the expression.

$\frac{p^{2} r^{4}}{q^{3}}$

$\frac{p^{2} r^{4}}{q^{3}}$

$\frac{p^{2} r^{4}}{q^{3}}$

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