Pre-Algebra Examples

$\frac{\frac{10 a^{3}}{b}}{\frac{4 a^{5} b}{3 b^{4}}}$

Step 1

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

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Step 1.1

Factor $b$ out of $4 a^{5} b$ .

$\frac{\frac{10 a^{3}}{b}}{\frac{b (4 a^{5})}{3 b^{4}}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $b$ out of $3 b^{4}$ .

$\frac{\frac{10 a^{3}}{b}}{\frac{b (4 a^{5})}{b (3 b^{3})}}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{10 a^{3}}{b}}{\frac{b (4 a^{5})}{b (3 b^{3})}}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{10 a^{3}}{b}}{\frac{4 a^{5}}{3 b^{3}}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{10 a^{3}}{b} \cdot \frac{3 b^{3}}{4 a^{5}}$

Step 3

Combine.

$\frac{10 a^{3} (3 b^{3})}{b (4 a^{5})}$

Step 4

Cancel the common factor of $10$ and $4$ .

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Step 4.1

Factor $2$ out of $10 a^{3} (3 b^{3})$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

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

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Step 6.1

Factor $b$ out of $5 (3 b^{3})$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Cancel the common factor.

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

Step 6.2.2

Rewrite the expression.

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

Step 7

Multiply $5$ by $3$ .

$\frac{15 b^{2}}{2 a^{2}}$