Pre-Algebra Examples

$\frac{5 a - 10}{3 a + 6} \cdot \frac{14 a + 28}{6 a - 12}$

Step 1

Factor $5$ out of $5 a - 10$ .

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Step 1.1

Factor $5$ out of $5 a$ .

$\frac{5 (a) - 10}{3 a + 6} \cdot \frac{14 a + 28}{6 a - 12}$

Step 1.2

Factor $5$ out of $- 10$ .

$\frac{5 a + 5 \cdot - 2}{3 a + 6} \cdot \frac{14 a + 28}{6 a - 12}$

Step 1.3

Factor $5$ out of $5 a + 5 \cdot - 2$ .

$\frac{5 (a - 2)}{3 a + 6} \cdot \frac{14 a + 28}{6 a - 12}$

Step 2

Factor $3$ out of $3 a + 6$ .

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Step 2.1

Factor $3$ out of $3 a$ .

$\frac{5 (a - 2)}{3 (a) + 6} \cdot \frac{14 a + 28}{6 a - 12}$

Step 2.2

Factor $3$ out of $6$ .

$\frac{5 (a - 2)}{3 a + 3 \cdot 2} \cdot \frac{14 a + 28}{6 a - 12}$

Step 2.3

Factor $3$ out of $3 a + 3 \cdot 2$ .

$\frac{5 (a - 2)}{3 (a + 2)} \cdot \frac{14 a + 28}{6 a - 12}$

Step 3

Factor $14$ out of $14 a + 28$ .

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Step 3.1

Factor $14$ out of $14 a$ .

$\frac{5 (a - 2)}{3 (a + 2)} \cdot \frac{14 (a) + 28}{6 a - 12}$

Step 3.2

Factor $14$ out of $28$ .

$\frac{5 (a - 2)}{3 (a + 2)} \cdot \frac{14 a + 14 \cdot 2}{6 a - 12}$

Step 3.3

Factor $14$ out of $14 a + 14 \cdot 2$ .

$\frac{5 (a - 2)}{3 (a + 2)} \cdot \frac{14 (a + 2)}{6 a - 12}$

Step 4

Factor $6$ out of $6 a - 12$ .

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Step 4.1

Factor $6$ out of $6 a$ .

$\frac{5 (a - 2)}{3 (a + 2)} \cdot \frac{14 (a + 2)}{6 (a) - 12}$

Step 4.2

Factor $6$ out of $- 12$ .

$\frac{5 (a - 2)}{3 (a + 2)} \cdot \frac{14 (a + 2)}{6 a + 6 \cdot - 2}$

Step 4.3

Factor $6$ out of $6 a + 6 \cdot - 2$ .

$\frac{5 (a - 2)}{3 (a + 2)} \cdot \frac{14 (a + 2)}{6 (a - 2)}$

Step 5

Cancel the common factor of $a - 2$ .

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Step 5.1

Factor $a - 2$ out of $5 (a - 2)$ .

$\frac{(a - 2) \cdot 5}{3 (a + 2)} \cdot \frac{14 (a + 2)}{6 (a - 2)}$

Step 5.2

Factor $a - 2$ out of $6 (a - 2)$ .

$\frac{(a - 2) \cdot 5}{3 (a + 2)} \cdot \frac{14 (a + 2)}{(a - 2) \cdot 6}$

Step 5.3

Cancel the common factor.

$\frac{(a - 2) \cdot 5}{3 (a + 2)} \cdot \frac{14 (a + 2)}{(a - 2) \cdot 6}$

Step 5.4

Rewrite the expression.

$\frac{5}{3 (a + 2)} \cdot \frac{14 (a + 2)}{6}$

Step 6

Cancel the common factor of $a + 2$ .

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Step 6.1

Factor $a + 2$ out of $3 (a + 2)$ .

$\frac{5}{(a + 2) \cdot 3} \cdot \frac{14 (a + 2)}{6}$

Step 6.2

Factor $a + 2$ out of $14 (a + 2)$ .

$\frac{5}{(a + 2) \cdot 3} \cdot \frac{(a + 2) \cdot 14}{6}$

Step 6.3

Cancel the common factor.

$\frac{5}{(a + 2) \cdot 3} \cdot \frac{(a + 2) \cdot 14}{6}$

Step 6.4

Rewrite the expression.

$\frac{5}{3} \cdot \frac{14}{6}$

Step 7

Multiply $\frac{5}{3}$ by $\frac{14}{6}$ .

$\frac{5 \cdot 14}{3 \cdot 6}$

Step 8

Multiply.

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Step 8.1

Multiply $5$ by $14$ .

$\frac{70}{3 \cdot 6}$

Step 8.2

Multiply $3$ by $6$ .

$\frac{70}{18}$

Step 9

Cancel the common factor of $70$ and $18$ .

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Step 9.1

Factor $2$ out of $70$ .

$\frac{2 (35)}{18}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $2$ out of $18$ .

$\frac{2 \cdot 35}{2 \cdot 9}$

Step 9.2.2

Cancel the common factor.

$\frac{2 \cdot 35}{2 \cdot 9}$

Step 9.2.3

Rewrite the expression.

$\frac{35}{9}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{35}{9}$

Decimal Form:

$3.\overline{8}$

Mixed Number Form:

$3 \frac{8}{9}$