Pre-Algebra Examples

$\frac{8 r - 24 s}{3 r - 6 s} \div \frac{12 s - 4 r}{2 r - 4 s}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{8 r - 24 s}{3 r - 6 s} \cdot \frac{2 r - 4 s}{12 s - 4 r}$

Step 2

Simplify terms.

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Step 2.1

Factor $8$ out of $8 r - 24 s$ .

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Step 2.1.1

Factor $8$ out of $8 r$ .

$\frac{8 (r) - 24 s}{3 r - 6 s} \cdot \frac{2 r - 4 s}{12 s - 4 r}$

Step 2.1.2

Factor $8$ out of $- 24 s$ .

$\frac{8 (r) + 8 (- 3 s)}{3 r - 6 s} \cdot \frac{2 r - 4 s}{12 s - 4 r}$

Step 2.1.3

Factor $8$ out of $8 (r) + 8 (- 3 s)$ .

$\frac{8 (r - 3 s)}{3 r - 6 s} \cdot \frac{2 r - 4 s}{12 s - 4 r}$

Step 2.2

Factor $3$ out of $3 r - 6 s$ .

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Step 2.2.1

Factor $3$ out of $3 r$ .

$\frac{8 (r - 3 s)}{3 (r) - 6 s} \cdot \frac{2 r - 4 s}{12 s - 4 r}$

Step 2.2.2

Factor $3$ out of $- 6 s$ .

$\frac{8 (r - 3 s)}{3 (r) + 3 (- 2 s)} \cdot \frac{2 r - 4 s}{12 s - 4 r}$

Step 2.2.3

Factor $3$ out of $3 (r) + 3 (- 2 s)$ .

$\frac{8 (r - 3 s)}{3 (r - 2 s)} \cdot \frac{2 r - 4 s}{12 s - 4 r}$

Step 2.3

Cancel the common factor of $2 r - 4 s$ and $12 s - 4 r$ .

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Step 2.3.1

Factor $2$ out of $2 r$ .

$\frac{8 (r - 3 s)}{3 (r - 2 s)} \cdot \frac{2 (r) - 4 s}{12 s - 4 r}$

Step 2.3.2

Factor $2$ out of $- 4 s$ .

$\frac{8 (r - 3 s)}{3 (r - 2 s)} \cdot \frac{2 (r) + 2 (- 2 s)}{12 s - 4 r}$

Step 2.3.3

Factor $2$ out of $2 (r) + 2 (- 2 s)$ .

$\frac{8 (r - 3 s)}{3 (r - 2 s)} \cdot \frac{2 (r - 2 s)}{12 s - 4 r}$

Step 2.3.4

Cancel the common factors.

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Step 2.3.4.1

Factor $2$ out of $12 s$ .

$\frac{8 (r - 3 s)}{3 (r - 2 s)} \cdot \frac{2 (r - 2 s)}{2 (6 s) - 4 r}$

Step 2.3.4.2

Factor $2$ out of $- 4 r$ .

$\frac{8 (r - 3 s)}{3 (r - 2 s)} \cdot \frac{2 (r - 2 s)}{2 (6 s) + 2 (- 2 r)}$

Step 2.3.4.3

Factor $2$ out of $2 (6 s) + 2 (- 2 r)$ .

$\frac{8 (r - 3 s)}{3 (r - 2 s)} \cdot \frac{2 (r - 2 s)}{2 (6 s - 2 r)}$

Step 2.3.4.4

Cancel the common factor.

$\frac{8 (r - 3 s)}{3 (r - 2 s)} \cdot \frac{2 (r - 2 s)}{2 (6 s - 2 r)}$

Step 2.3.4.5

Rewrite the expression.

$\frac{8 (r - 3 s)}{3 (r - 2 s)} \cdot \frac{r - 2 s}{6 s - 2 r}$

Step 2.4

Cancel the common factor of $r - 2 s$ .

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Step 2.4.1

Factor $r - 2 s$ out of $3 (r - 2 s)$ .

$\frac{8 (r - 3 s)}{(r - 2 s) \cdot 3} \cdot \frac{r - 2 s}{6 s - 2 r}$

Step 2.4.2

Cancel the common factor.

$\frac{8 (r - 3 s)}{(r - 2 s) \cdot 3} \cdot \frac{r - 2 s}{6 s - 2 r}$

Step 2.4.3

Rewrite the expression.

$\frac{8 (r - 3 s)}{3} \cdot \frac{1}{6 s - 2 r}$

Step 2.5

Multiply $\frac{8 (r - 3 s)}{3}$ by $\frac{1}{6 s - 2 r}$ .

$\frac{8 (r - 3 s)}{3 (6 s - 2 r)}$

Step 2.6

Cancel the common factor of $8$ and $6 s - 2 r$ .

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Step 2.6.1

Factor $2$ out of $8 (r - 3 s)$ .

$\frac{2 (4 (r - 3 s))}{3 (6 s - 2 r)}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $2$ out of $3 (6 s - 2 r)$ .

$\frac{2 (4 (r - 3 s))}{2 (3 (3 s - r))}$

Step 2.6.2.2

Cancel the common factor.

$\frac{2 (4 (r - 3 s))}{2 (3 (3 s - r))}$

Step 2.6.2.3

Rewrite the expression.

$\frac{4 (r - 3 s)}{3 (3 s - r)}$

Step 2.7

Cancel the common factor of $r - 3 s$ and $3 s - r$ .

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Step 2.7.1

Factor $- 1$ out of $r$ .

$\frac{4 (- 1 (- r) - 3 s)}{3 (3 s - r)}$

Step 2.7.2

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

$\frac{4 (- 1 (- r) - (3 s))}{3 (3 s - r)}$

Step 2.7.3

Factor $- 1$ out of $- 1 (- r) - (3 s)$ .

$\frac{4 (- 1 (- r + 3 s))}{3 (3 s - r)}$

Step 2.7.4

Reorder terms.

$\frac{4 (- 1 (- r + 3 s))}{3 (- r + 3 s)}$

Step 2.7.5

Cancel the common factor.

$\frac{4 (- 1 (- r + 3 s))}{3 (- r + 3 s)}$

Step 2.7.6

Rewrite the expression.

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

Step 3

Multiply $4$ by $- 1$ .

$\frac{- 4}{3}$

Step 4

Move the negative in front of the fraction.

$- \frac{4}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{4}{3}$

Decimal Form:

$- 1.\overline{3}$

Mixed Number Form:

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