Pre-Algebra Examples

$\frac{12 x - 8}{15} \cdot \frac{6}{2 - 3 x}$

Step 1

Simplify terms.

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Step 1.1

Factor $4$ out of $12 x - 8$ .

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Step 1.1.1

Factor $4$ out of $12 x$ .

$\frac{4 (3 x) - 8}{15} \cdot \frac{6}{2 - 3 x}$

Step 1.1.2

Factor $4$ out of $- 8$ .

$\frac{4 (3 x) + 4 (- 2)}{15} \cdot \frac{6}{2 - 3 x}$

Step 1.1.3

Factor $4$ out of $4 (3 x) + 4 (- 2)$ .

$\frac{4 (3 x - 2)}{15} \cdot \frac{6}{2 - 3 x}$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Factor $3$ out of $15$ .

$\frac{4 (3 x - 2)}{3 (5)} \cdot \frac{6}{2 - 3 x}$

Step 1.2.2

Factor $3$ out of $6$ .

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

Step 1.2.3

Cancel the common factor.

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

Step 1.2.4

Rewrite the expression.

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

Step 1.3

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

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

Step 1.4

Multiply $2$ by $4$ .

$\frac{8 (3 x - 2)}{5 (2 - 3 x)}$

Step 1.5

Cancel the common factor of $3 x - 2$ and $2 - 3 x$ .

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Step 1.5.1

Factor $- 1$ out of $3 x$ .

$\frac{8 (- (- 3 x) - 2)}{5 (2 - 3 x)}$

Step 1.5.2

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{8 (- (- 3 x) - 1 (2))}{5 (2 - 3 x)}$

Step 1.5.3

Factor $- 1$ out of $- (- 3 x) - 1 (2)$ .

$\frac{8 (- (- 3 x + 2))}{5 (2 - 3 x)}$

Step 1.5.4

Rewrite $- (- 3 x + 2)$ as $- 1 (- 3 x + 2)$ .

$\frac{8 (- 1 (- 3 x + 2))}{5 (2 - 3 x)}$

Step 1.5.5

Reorder terms.

$\frac{8 (- 1 (- 3 x + 2))}{5 (- 3 x + 2)}$

Step 1.5.6

Cancel the common factor.

$\frac{8 (- 1 (- 3 x + 2))}{5 (- 3 x + 2)}$

Step 1.5.7

Rewrite the expression.

$\frac{8 \cdot (- 1)}{5}$

Step 2

Multiply $8$ by $- 1$ .

$\frac{- 8}{5}$

Step 3

Move the negative in front of the fraction.

$- \frac{8}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{8}{5}$

Decimal Form:

$- 1.6$

Mixed Number Form:

$- 1 \frac{3}{5}$