Basic Math Examples

$\frac{80 r^{2}}{9 r^{3} - 27 r^{2}} \div \frac{1}{3 - r}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{80 r^{2}}{9 r^{3} - 27 r^{2}} (3 - r)$

Step 2

Simplify terms.

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Step 2.1

Factor $9 r^{2}$ out of $9 r^{3} - 27 r^{2}$ .

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Step 2.1.1

Factor $9 r^{2}$ out of $9 r^{3}$ .

$\frac{80 r^{2}}{9 r^{2} (r) - 27 r^{2}} (3 - r)$

Step 2.1.2

Factor $9 r^{2}$ out of $- 27 r^{2}$ .

$\frac{80 r^{2}}{9 r^{2} (r) + 9 r^{2} (- 3)} (3 - r)$

Step 2.1.3

Factor $9 r^{2}$ out of $9 r^{2} (r) + 9 r^{2} (- 3)$ .

$\frac{80 r^{2}}{9 r^{2} (r - 3)} (3 - r)$

Step 2.2

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

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Step 2.2.1

Cancel the common factor.

$\frac{80 r^{2}}{9 r^{2} (r - 3)} (3 - r)$

Step 2.2.2

Rewrite the expression.

$\frac{80}{9 (r - 3)} (3 - r)$

Step 2.3

Multiply $\frac{80}{9 (r - 3)}$ by $3 - r$ .

$\frac{80 (3 - r)}{9 (r - 3)}$

Step 2.4

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

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Step 2.4.1

Rewrite $3$ as $- 1 (- 3)$ .

$\frac{80 (- 1 (- 3) - r)}{9 (r - 3)}$

Step 2.4.2

Factor $- 1$ out of $- r$ .

$\frac{80 (- 1 (- 3) - (r))}{9 (r - 3)}$

Step 2.4.3

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

$\frac{80 (- 1 (- 3 + r))}{9 (r - 3)}$

Step 2.4.4

Reorder terms.

$\frac{80 (- 1 (r - 3))}{9 (r - 3)}$

Step 2.4.5

Cancel the common factor.

$\frac{80 (- 1 (r - 3))}{9 (r - 3)}$

Step 2.4.6

Rewrite the expression.

$\frac{80 \cdot (- 1)}{9}$

Step 3

Multiply $80$ by $- 1$ .

$\frac{- 80}{9}$

Step 4

Move the negative in front of the fraction.

$- \frac{80}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{80}{9}$

Decimal Form:

$- 8.\overline{8}$

Mixed Number Form:

$- 8 \frac{8}{9}$