Basic Math Examples

$\frac{5 (r + 2)}{10 r - 70} \cdot \frac{4 (7 - r)}{8 r + 16}$

Step 1

Factor $10$ out of $10 r - 70$ .

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Step 1.1

Factor $10$ out of $10 r$ .

$\frac{5 (r + 2)}{10 (r) - 70} \cdot \frac{4 (7 - r)}{8 r + 16}$

Step 1.2

Factor $10$ out of $- 70$ .

$\frac{5 (r + 2)}{10 r + 10 \cdot - 7} \cdot \frac{4 (7 - r)}{8 r + 16}$

Step 1.3

Factor $10$ out of $10 r + 10 \cdot - 7$ .

$\frac{5 (r + 2)}{10 (r - 7)} \cdot \frac{4 (7 - r)}{8 r + 16}$

Step 2

Factor $8$ out of $8 r + 16$ .

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Step 2.1

Factor $8$ out of $8 r$ .

$\frac{5 (r + 2)}{10 (r - 7)} \cdot \frac{4 (7 - r)}{8 (r) + 16}$

Step 2.2

Factor $8$ out of $16$ .

$\frac{5 (r + 2)}{10 (r - 7)} \cdot \frac{4 (7 - r)}{8 r + 8 \cdot 2}$

Step 2.3

Factor $8$ out of $8 r + 8 \cdot 2$ .

$\frac{5 (r + 2)}{10 (r - 7)} \cdot \frac{4 (7 - r)}{8 (r + 2)}$

Step 3

Cancel the common factor of $r + 2$ .

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Step 3.1

Factor $r + 2$ out of $5 (r + 2)$ .

$\frac{(r + 2) \cdot 5}{10 (r - 7)} \cdot \frac{4 (7 - r)}{8 (r + 2)}$

Step 3.2

Factor $r + 2$ out of $8 (r + 2)$ .

$\frac{(r + 2) \cdot 5}{10 (r - 7)} \cdot \frac{4 (7 - r)}{(r + 2) \cdot 8}$

Step 3.3

Cancel the common factor.

$\frac{(r + 2) \cdot 5}{10 (r - 7)} \cdot \frac{4 (7 - r)}{(r + 2) \cdot 8}$

Step 3.4

Rewrite the expression.

$\frac{5}{10 (r - 7)} \cdot \frac{4 (7 - r)}{8}$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Factor $2$ out of $10 (r - 7)$ .

$\frac{5}{2 (5 (r - 7))} \cdot \frac{4 (7 - r)}{8}$

Step 4.2

Factor $2$ out of $4 (7 - r)$ .

$\frac{5}{2 (5 (r - 7))} \cdot \frac{2 (2 (7 - r))}{8}$

Step 4.3

Cancel the common factor.

$\frac{5}{2 (5 (r - 7))} \cdot \frac{2 (2 (7 - r))}{8}$

Step 4.4

Rewrite the expression.

$\frac{5}{5 (r - 7)} \cdot \frac{2 (7 - r)}{8}$

Step 5

Multiply $\frac{5}{5 (r - 7)}$ by $\frac{2 (7 - r)}{8}$ .

$\frac{5 (2 (7 - r))}{5 (r - 7) \cdot 8}$

Step 6

Multiply.

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Step 6.1

Multiply $2$ by $5$ .

$\frac{10 (7 - r)}{5 (r - 7) \cdot 8}$

Step 6.2

Multiply $8$ by $5$ .

$\frac{10 (7 - r)}{40 (r - 7)}$

Step 7

Cancel the common factors.

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Step 7.1

Factor $10$ out of $40 (r - 7)$ .

$\frac{10 (7 - r)}{10 (4 (r - 7))}$

Step 7.2

Cancel the common factor.

$\frac{10 (7 - r)}{10 (4 (r - 7))}$

Step 7.3

Rewrite the expression.

$\frac{7 - r}{4 (r - 7)}$

Step 8

Cancel the common factor of $7 - r$ and $r - 7$ .

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Step 8.1

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{- 1 (- 7) - r}{4 (r - 7)}$

Step 8.2

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

$\frac{- 1 (- 7) - (r)}{4 (r - 7)}$

Step 8.3

Factor $- 1$ out of $- 1 (- 7) - (r)$ .

$\frac{- 1 (- 7 + r)}{4 (r - 7)}$

Step 8.4

Reorder terms.

$\frac{- 1 (r - 7)}{4 (r - 7)}$

Step 8.5

Cancel the common factor.

$\frac{- 1 (r - 7)}{4 (r - 7)}$

Step 8.6

Rewrite the expression.

$\frac{- 1}{4}$

Step 9

Move the negative in front of the fraction.

$- \frac{1}{4}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{4}$

Decimal Form:

$- 0.25$