Basic Math Examples

$\frac{\frac{7 p q^{2}}{10 r^{2} s}}{\frac{14 q^{5}}{5 r^{3} s^{4}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{7 p q^{2}}{10 r^{2} s} \cdot \frac{5 r^{3} s^{4}}{14 q^{5}}$

Step 2

Combine.

$\frac{7 p q^{2} (5 r^{3} s^{4})}{10 r^{2} s (14 q^{5})}$

Step 3

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

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Step 3.1

Factor $7$ out of $7 p q^{2} (5 r^{3} s^{4})$ .

$\frac{7 (p q^{2} (5 r^{3} s^{4}))}{10 r^{2} s (14 q^{5})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $7$ out of $10 r^{2} s (14 q^{5})$ .

$\frac{7 (p q^{2} (5 r^{3} s^{4}))}{7 (10 r^{2} s (2 q^{5}))}$

Step 3.2.2

Cancel the common factor.

$\frac{7 (p q^{2} (5 r^{3} s^{4}))}{7 (10 r^{2} s (2 q^{5}))}$

Step 3.2.3

Rewrite the expression.

$\frac{p q^{2} (5 r^{3} s^{4})}{10 r^{2} s (2 q^{5})}$

Step 4

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

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Step 4.1

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

$\frac{q^{2} (p (5 r^{3} s^{4}))}{10 r^{2} s (2 q^{5})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $q^{2}$ out of $10 r^{2} s (2 q^{5})$ .

$\frac{q^{2} (p (5 r^{3} s^{4}))}{q^{2} (10 r^{2} s (2 q^{3}))}$

Step 4.2.2

Cancel the common factor.

$\frac{q^{2} (p (5 r^{3} s^{4}))}{q^{2} (10 r^{2} s (2 q^{3}))}$

Step 4.2.3

Rewrite the expression.

$\frac{p (5 r^{3} s^{4})}{10 r^{2} s (2 q^{3})}$

Step 5

Cancel the common factor of $5$ and $10$ .

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Step 5.1

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

$\frac{5 (p (r^{3} s^{4}))}{10 r^{2} s (2 q^{3})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $5$ out of $10 r^{2} s (2 q^{3})$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 8

Simplify the expression.

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Step 8.1

Multiply $2$ by $2$ .

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

Step 8.2

Raise $2$ to the power of $2$ .

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