Finite Math Examples

$\frac{\frac{14 r^{2} s}{5 p q^{2}}}{\frac{7 r^{5} s^{4}}{20 q^{4}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{14 r^{2} s}{5 p q^{2}} \cdot \frac{20 q^{4}}{7 r^{5} s^{4}}$

Step 2

Combine.

$\frac{14 r^{2} s (20 q^{4})}{5 p q^{2} (7 r^{5} s^{4})}$

Step 3

Cancel the common factor of $14$ and $7$ .

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Step 3.1

Factor $7$ out of $14 r^{2} s (20 q^{4})$ .

$\frac{7 (2 r^{2} s (20 q^{4}))}{5 p q^{2} (7 r^{5} s^{4})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $7$ out of $5 p q^{2} (7 r^{5} s^{4})$ .

$\frac{7 (2 r^{2} s (20 q^{4}))}{7 (5 p q^{2} (r^{5} s^{4}))}$

Step 3.2.2

Cancel the common factor.

$\frac{7 (2 r^{2} s (20 q^{4}))}{7 (5 p q^{2} (r^{5} s^{4}))}$

Step 3.2.3

Rewrite the expression.

$\frac{2 r^{2} s (20 q^{4})}{5 p q^{2} (r^{5} s^{4})}$

Step 4

Cancel the common factor of $r^{2}$ and $r^{5}$ .

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Step 4.1

Factor $r^{2}$ out of $2 r^{2} s (20 q^{4})$ .

$\frac{r^{2} (2 s (20 q^{4}))}{5 p q^{2} (r^{5} s^{4})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $r^{2}$ out of $5 p q^{2} (r^{5} s^{4})$ .

$\frac{r^{2} (2 s (20 q^{4}))}{r^{2} (5 p q^{2} (r^{3} s^{4}))}$

Step 4.2.2

Cancel the common factor.

$\frac{r^{2} (2 s (20 q^{4}))}{r^{2} (5 p q^{2} (r^{3} s^{4}))}$

Step 4.2.3

Rewrite the expression.

$\frac{2 s (20 q^{4})}{5 p q^{2} (r^{3} s^{4})}$

Step 5

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

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Step 5.1

Factor $s$ out of $2 s (20 q^{4})$ .

$\frac{s (2 (20 q^{4}))}{5 p q^{2} (r^{3} s^{4})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $s$ out of $5 p q^{2} (r^{3} s^{4})$ .

$\frac{s (2 (20 q^{4}))}{s (5 p q^{2} (r^{3} s^{3}))}$

Step 5.2.2

Cancel the common factor.

$\frac{s (2 (20 q^{4}))}{s (5 p q^{2} (r^{3} s^{3}))}$

Step 5.2.3

Rewrite the expression.

$\frac{2 (20 q^{4})}{5 p q^{2} (r^{3} s^{3})}$

Step 6

Cancel the common factor of $20$ and $5$ .

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Step 6.1

Factor $5$ out of $2 (20 q^{4})$ .

$\frac{5 (2 (4 q^{4}))}{5 p q^{2} (r^{3} s^{3})}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $5$ out of $5 p q^{2} (r^{3} s^{3})$ .

$\frac{5 (2 (4 q^{4}))}{5 (p q^{2} (r^{3} s^{3}))}$

Step 6.2.2

Cancel the common factor.

$\frac{5 (2 (4 q^{4}))}{5 (p q^{2} (r^{3} s^{3}))}$

Step 6.2.3

Rewrite the expression.

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

Step 7

Cancel the common factor of $q^{4}$ and $q^{2}$ .

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Step 7.1

Factor $q^{2}$ out of $2 (4 q^{4})$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $q^{2}$ out of $p q^{2} (r^{3} s^{3})$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 8

Multiply $2$ by $4$ .

$\frac{8 q^{2}}{p r^{3} s^{3}}$