Basic Math Examples

$\frac{\frac{6 b^{5}}{5 c^{5} d^{3}}}{\frac{3 a b^{2}}{20 c^{3} d}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{6 b^{5}}{5 c^{5} d^{3}} \cdot \frac{20 c^{3} d}{3 a b^{2}}$

Step 2

Combine.

$\frac{6 b^{5} (20 c^{3} d)}{5 c^{5} d^{3} (3 a b^{2})}$

Step 3

Cancel the common factor of $6$ and $3$ .

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Step 3.1

Factor $3$ out of $6 b^{5} (20 c^{3} d)$ .

$\frac{3 (2 b^{5} (20 c^{3} d))}{5 c^{5} d^{3} (3 a b^{2})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $5 c^{5} d^{3} (3 a b^{2})$ .

$\frac{3 (2 b^{5} (20 c^{3} d))}{3 (5 c^{5} d^{3} (a b^{2}))}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (2 b^{5} (20 c^{3} d))}{3 (5 c^{5} d^{3} (a b^{2}))}$

Step 3.2.3

Rewrite the expression.

$\frac{2 b^{5} (20 c^{3} d)}{5 c^{5} d^{3} (a b^{2})}$

Step 4

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

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Step 4.1

Factor $b^{2}$ out of $2 b^{5} (20 c^{3} d)$ .

$\frac{b^{2} (2 b^{3} (20 c^{3} d))}{5 c^{5} d^{3} (a b^{2})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $b^{2}$ out of $5 c^{5} d^{3} (a b^{2})$ .

$\frac{b^{2} (2 b^{3} (20 c^{3} d))}{b^{2} (5 c^{5} d^{3} (a))}$

Step 4.2.2

Cancel the common factor.

$\frac{b^{2} (2 b^{3} (20 c^{3} d))}{b^{2} (5 c^{5} d^{3} (a))}$

Step 4.2.3

Rewrite the expression.

$\frac{2 b^{3} (20 c^{3} d)}{5 c^{5} d^{3} (a)}$

Step 5

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

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Step 5.1

Factor $5$ out of $2 b^{3} (20 c^{3} d)$ .

$\frac{5 (2 b^{3} (4 c^{3} d))}{5 c^{5} d^{3} (a)}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $5$ out of $5 c^{5} d^{3} (a)$ .

$\frac{5 (2 b^{3} (4 c^{3} d))}{5 (c^{5} d^{3} (a))}$

Step 5.2.2

Cancel the common factor.

$\frac{5 (2 b^{3} (4 c^{3} d))}{5 (c^{5} d^{3} (a))}$

Step 5.2.3

Rewrite the expression.

$\frac{2 b^{3} (4 c^{3} d)}{c^{5} d^{3} (a)}$

Step 6

Cancel the common factor of $c^{3}$ and $c^{5}$ .

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Step 6.1

Factor $c^{3}$ out of $2 b^{3} (4 c^{3} d)$ .

$\frac{c^{3} (2 b^{3} (4 d))}{c^{5} d^{3} (a)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $c^{3}$ out of $c^{5} d^{3} (a)$ .

$\frac{c^{3} (2 b^{3} (4 d))}{c^{3} (c^{2} d^{3} a)}$

Step 6.2.2

Cancel the common factor.

$\frac{c^{3} (2 b^{3} (4 d))}{c^{3} (c^{2} d^{3} a)}$

Step 6.2.3

Rewrite the expression.

$\frac{2 b^{3} (4 d)}{c^{2} d^{3} a}$

Step 7

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

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Step 7.1

Factor $d$ out of $2 b^{3} (4 d)$ .

$\frac{d (2 b^{3} \cdot (4))}{c^{2} d^{3} a}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $d$ out of $c^{2} d^{3} a$ .

$\frac{d (2 b^{3} \cdot (4))}{d (c^{2} d^{2} a)}$

Step 7.2.2

Cancel the common factor.

$\frac{d (2 b^{3} \cdot (4))}{d (c^{2} d^{2} a)}$

Step 7.2.3

Rewrite the expression.

$\frac{2 b^{3} \cdot (4)}{c^{2} d^{2} a}$

Step 8

Multiply $4$ by $2$ .

$\frac{8 b^{3}}{c^{2} d^{2} a}$