Pre-Algebra Examples

$\frac{\frac{10 c^{3} d}{7 a b^{2}}}{\frac{5 c^{4} d^{4}}{28 b^{4}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{10 c^{3} d}{7 a b^{2}} \cdot \frac{28 b^{4}}{5 c^{4} d^{4}}$

Step 2

Combine.

$\frac{10 c^{3} d (28 b^{4})}{7 a b^{2} (5 c^{4} d^{4})}$

Step 3

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

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Step 3.1

Factor $5$ out of $10 c^{3} d (28 b^{4})$ .

$\frac{5 (2 c^{3} d (28 b^{4}))}{7 a b^{2} (5 c^{4} d^{4})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $5$ out of $7 a b^{2} (5 c^{4} d^{4})$ .

$\frac{5 (2 c^{3} d (28 b^{4}))}{5 (7 a b^{2} (c^{4} d^{4}))}$

Step 3.2.2

Cancel the common factor.

$\frac{5 (2 c^{3} d (28 b^{4}))}{5 (7 a b^{2} (c^{4} d^{4}))}$

Step 3.2.3

Rewrite the expression.

$\frac{2 c^{3} d (28 b^{4})}{7 a b^{2} (c^{4} d^{4})}$

Step 4

Cancel the common factor of $c^{3}$ and $c^{4}$ .

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Step 4.1

Factor $c^{3}$ out of $2 c^{3} d (28 b^{4})$ .

$\frac{c^{3} (2 d (28 b^{4}))}{7 a b^{2} (c^{4} d^{4})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $c^{3}$ out of $7 a b^{2} (c^{4} d^{4})$ .

$\frac{c^{3} (2 d (28 b^{4}))}{c^{3} (7 a b^{2} (c d^{4}))}$

Step 4.2.2

Cancel the common factor.

$\frac{c^{3} (2 d (28 b^{4}))}{c^{3} (7 a b^{2} (c d^{4}))}$

Step 4.2.3

Rewrite the expression.

$\frac{2 d (28 b^{4})}{7 a b^{2} (c d^{4})}$

Step 5

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

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Step 5.1

Factor $d$ out of $2 d (28 b^{4})$ .

$\frac{d (2 (28 b^{4}))}{7 a b^{2} (c d^{4})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $d$ out of $7 a b^{2} (c d^{4})$ .

$\frac{d (2 (28 b^{4}))}{d (7 a b^{2} (c d^{3}))}$

Step 5.2.2

Cancel the common factor.

$\frac{d (2 (28 b^{4}))}{d (7 a b^{2} (c d^{3}))}$

Step 5.2.3

Rewrite the expression.

$\frac{2 (28 b^{4})}{7 a b^{2} (c d^{3})}$

Step 6

Cancel the common factor of $28$ and $7$ .

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Step 6.1

Factor $7$ out of $2 (28 b^{4})$ .

$\frac{7 (2 (4 b^{4}))}{7 a b^{2} (c d^{3})}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $7$ out of $7 a b^{2} (c d^{3})$ .

$\frac{7 (2 (4 b^{4}))}{7 (a b^{2} (c d^{3}))}$

Step 6.2.2

Cancel the common factor.

$\frac{7 (2 (4 b^{4}))}{7 (a b^{2} (c d^{3}))}$

Step 6.2.3

Rewrite the expression.

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 8

Multiply $2$ by $4$ .

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