Basic Math Examples

$\frac{1}{8 - 2 a} \div \frac{5}{3 a - 12}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{1}{8 - 2 a} \cdot \frac{3 a - 12}{5}$

Step 2

Factor $2$ out of $8 - 2 a$ .

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Step 2.1

Factor $2$ out of $8$ .

$\frac{1}{2 (4) - 2 a} \cdot \frac{3 a - 12}{5}$

Step 2.2

Factor $2$ out of $- 2 a$ .

$\frac{1}{2 (4) + 2 (- a)} \cdot \frac{3 a - 12}{5}$

Step 2.3

Factor $2$ out of $2 (4) + 2 (- a)$ .

$\frac{1}{2 (4 - a)} \cdot \frac{3 a - 12}{5}$

Step 3

Factor $3$ out of $3 a - 12$ .

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Step 3.1

Factor $3$ out of $3 a$ .

$\frac{1}{2 (4 - a)} \cdot \frac{3 (a) - 12}{5}$

Step 3.2

Factor $3$ out of $- 12$ .

$\frac{1}{2 (4 - a)} \cdot \frac{3 a + 3 \cdot - 4}{5}$

Step 3.3

Factor $3$ out of $3 a + 3 \cdot - 4$ .

$\frac{1}{2 (4 - a)} \cdot \frac{3 (a - 4)}{5}$

Step 4

Multiply $\frac{1}{2 (4 - a)} \cdot \frac{3 (a - 4)}{5}$ .

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Step 4.1

Multiply $\frac{1}{2 (4 - a)}$ by $\frac{3 (a - 4)}{5}$ .

$\frac{3 (a - 4)}{2 (4 - a) \cdot 5}$

Step 4.2

Multiply $5$ by $2$ .

$\frac{3 (a - 4)}{10 (4 - a)}$

Step 5

Cancel the common factor of $a - 4$ and $4 - a$ .

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Step 5.1

Factor $- 1$ out of $a$ .

$\frac{3 (- 1 (- a) - 4)}{10 (4 - a)}$

Step 5.2

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{3 (- 1 (- a) - 1 (4))}{10 (4 - a)}$

Step 5.3

Factor $- 1$ out of $- 1 (- a) - 1 (4)$ .

$\frac{3 (- 1 (- a + 4))}{10 (4 - a)}$

Step 5.4

Reorder terms.

$\frac{3 (- 1 (- a + 4))}{10 (- a + 4)}$

Step 5.5

Cancel the common factor.

$\frac{3 (- 1 (- a + 4))}{10 (- a + 4)}$

Step 5.6

Rewrite the expression.

$\frac{3 \cdot (- 1)}{10}$

Step 6

Multiply $3$ by $- 1$ .

$\frac{- 3}{10}$

Step 7

Move the negative in front of the fraction.

$- \frac{3}{10}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{10}$

Decimal Form:

$- 0.3$