Pre-Algebra Examples

$\frac{9 (b^{4})}{c} \div \frac{15 b^{5} c}{2 c} \cdot 5$

Step 1

Reduce the expression $\frac{15 b^{5} c}{2 c}$ by cancelling the common factors.

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Step 1.1

Cancel the common factor.

$\frac{9 b^{4}}{c} \div \frac{15 b^{5} c}{2 c} \cdot 5$

Step 1.2

Rewrite the expression.

$\frac{9 b^{4}}{c} \div \frac{15 b^{5}}{2} \cdot 5$

Step 2

To divide by a fraction, multiply by its reciprocal.

$\frac{9 b^{4}}{c} \cdot \frac{2}{15 b^{5}} \cdot 5$

Step 3

Combine.

$\frac{9 b^{4} \cdot 2}{c (15 b^{5})} \cdot 5$

Step 4

Multiply $2$ by $9$ .

$\frac{18 b^{4}}{c (15 b^{5})} \cdot 5$

Step 5

Cancel the common factor of $5$ .

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Step 5.1

Factor $5$ out of $c \cdot 15 b^{5}$ .

$\frac{18 b^{4}}{5 (c \cdot 3 b^{5})} \cdot 5$

Step 5.2

Cancel the common factor.

$\frac{18 b^{4}}{5 (c \cdot 3 b^{5})} \cdot 5$

Step 5.3

Rewrite the expression.

$\frac{18 b^{4}}{c \cdot 3 b^{5}}$

Step 6

Cancel the common factor of $18$ and $3$ .

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Step 6.1

Factor $3$ out of $18 b^{4}$ .

$\frac{3 (6 b^{4})}{c \cdot 3 b^{5}}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $c \cdot 3 b^{5}$ .

$\frac{3 (6 b^{4})}{3 (c b^{5})}$

Step 6.2.2

Cancel the common factor.

$\frac{3 (6 b^{4})}{3 (c b^{5})}$

Step 6.2.3

Rewrite the expression.

$\frac{6 b^{4}}{c b^{5}}$

Step 7

Cancel the common factor of $b^{4}$ and $b^{5}$ .

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Step 7.1

Factor $b^{4}$ out of $6 b^{4}$ .

$\frac{b^{4} \cdot 6}{c b^{5}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

$\frac{b^{4} \cdot 6}{b^{4} (c b)}$

Step 7.2.2

Cancel the common factor.

$\frac{b^{4} \cdot 6}{b^{4} (c b)}$

Step 7.2.3

Rewrite the expression.

$\frac{6}{c b}$