Basic Math Examples

$\frac{25 a^{3}}{10 a^{3} - 20 a^{2}} \div \frac{- a}{4 a - 8}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{25 a^{3}}{10 a^{3} - 20 a^{2}} \cdot \frac{4 a - 8}{- a}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $a$ .

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Step 2.1.1

Factor $a$ out of $25 a^{3}$ .

$\frac{a (25 a^{2})}{10 a^{3} - 20 a^{2}} \cdot \frac{4 a - 8}{- a}$

Step 2.1.2

Factor $a$ out of $- a$ .

$\frac{a (25 a^{2})}{10 a^{3} - 20 a^{2}} \cdot \frac{4 a - 8}{a \cdot - 1}$

Step 2.1.3

Cancel the common factor.

$\frac{a (25 a^{2})}{10 a^{3} - 20 a^{2}} \cdot \frac{4 a - 8}{a \cdot - 1}$

Step 2.1.4

Rewrite the expression.

$\frac{25 a^{2}}{10 a^{3} - 20 a^{2}} \cdot \frac{4 a - 8}{- 1}$

Step 2.2

Multiply $\frac{25 a^{2}}{10 a^{3} - 20 a^{2}}$ by $\frac{4 a - 8}{- 1}$ .

$\frac{25 a^{2} (4 a - 8)}{(10 a^{3} - 20 a^{2}) \cdot - 1}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $4$ out of $4 a - 8$ .

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Step 3.1.1

Factor $4$ out of $4 a$ .

$\frac{25 a^{2} (4 (a) - 8)}{(10 a^{3} - 20 a^{2}) \cdot - 1}$

Step 3.1.2

Factor $4$ out of $- 8$ .

$\frac{25 a^{2} (4 a + 4 \cdot - 2)}{(10 a^{3} - 20 a^{2}) \cdot - 1}$

Step 3.1.3

Factor $4$ out of $4 a + 4 \cdot - 2$ .

$\frac{25 a^{2} (4 (a - 2))}{(10 a^{3} - 20 a^{2}) \cdot - 1}$

$\frac{25 a^{2} \cdot 4 (a - 2)}{(10 a^{3} - 20 a^{2}) \cdot - 1}$

Step 3.2

Multiply $4$ by $25$ .

$\frac{100 a^{2} (a - 2)}{(10 a^{3} - 20 a^{2}) \cdot - 1}$

Step 4

Simplify the denominator.

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Step 4.1

Factor $10 a^{2}$ out of $10 a^{3} - 20 a^{2}$ .

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Step 4.1.1

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

$\frac{100 a^{2} (a - 2)}{(10 a^{2} (a) - 20 a^{2}) \cdot - 1}$

Step 4.1.2

Factor $10 a^{2}$ out of $- 20 a^{2}$ .

$\frac{100 a^{2} (a - 2)}{(10 a^{2} (a) + 10 a^{2} (- 2)) \cdot - 1}$

Step 4.1.3

Factor $10 a^{2}$ out of $10 a^{2} (a) + 10 a^{2} (- 2)$ .

$\frac{100 a^{2} (a - 2)}{10 a^{2} (a - 2) \cdot - 1}$

Step 4.2

Multiply $- 1$ by $10$ .

$\frac{100 a^{2} (a - 2)}{- 10 a^{2} (a - 2)}$

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

Cancel the common factor of $100$ and $- 10$ .

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Step 5.1.1

Factor $10$ out of $100 a^{2} (a - 2)$ .

$\frac{10 (10 a^{2} (a - 2))}{- 10 a^{2} (a - 2)}$

Step 5.1.2

Cancel the common factors.

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Step 5.1.2.1

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

$\frac{10 (10 a^{2} (a - 2))}{10 (- a^{2} (a - 2))}$

Step 5.1.2.2

Cancel the common factor.

$\frac{10 (10 a^{2} (a - 2))}{10 (- a^{2} (a - 2))}$

Step 5.1.2.3

Rewrite the expression.

$\frac{10 a^{2} (a - 2)}{- a^{2} (a - 2)}$

Step 5.2

Cancel the common factor of $a^{2}$ .

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Step 5.2.1

Cancel the common factor.

$\frac{10 a^{2} (a - 2)}{- a^{2} (a - 2)}$

Step 5.2.2

Rewrite the expression.

$\frac{10 (a - 2)}{- (a - 2)}$

Step 5.3

Cancel the common factor of $a - 2$ .

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Step 5.3.1

Cancel the common factor.

$\frac{10 (a - 2)}{- (a - 2)}$

Step 5.3.2

Rewrite the expression.

$\frac{10}{- 1}$

Step 5.3.3

Move the negative one from the denominator of $\frac{10}{- 1}$ .

$- 1 \cdot 10$

Step 5.4

Multiply $- 1$ by $10$ .

$- 10$