Pre-Algebra Examples

$\frac{6 a - 12}{9 a + 27} \div \frac{22 a - 44}{7 a + 21}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{6 a - 12}{9 a + 27} \cdot \frac{7 a + 21}{22 a - 44}$

Step 2

Cancel the common factor of $6 a - 12$ and $9 a + 27$ .

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Step 2.1

Factor $3$ out of $6 a$ .

$\frac{3 (2 a) - 12}{9 a + 27} \cdot \frac{7 a + 21}{22 a - 44}$

Step 2.2

Factor $3$ out of $- 12$ .

$\frac{3 (2 a) + 3 (- 4)}{9 a + 27} \cdot \frac{7 a + 21}{22 a - 44}$

Step 2.3

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

$\frac{3 (2 a - 4)}{9 a + 27} \cdot \frac{7 a + 21}{22 a - 44}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

Factor $3$ out of $9 a$ .

$\frac{3 (2 a - 4)}{3 (3 a) + 27} \cdot \frac{7 a + 21}{22 a - 44}$

Step 2.4.2

Factor $3$ out of $27$ .

$\frac{3 (2 a - 4)}{3 (3 a) + 3 (9)} \cdot \frac{7 a + 21}{22 a - 44}$

Step 2.4.3

Factor $3$ out of $3 (3 a) + 3 (9)$ .

$\frac{3 (2 a - 4)}{3 (3 a + 9)} \cdot \frac{7 a + 21}{22 a - 44}$

Step 2.4.4

Cancel the common factor.

$\frac{3 (2 a - 4)}{3 (3 a + 9)} \cdot \frac{7 a + 21}{22 a - 44}$

Step 2.4.5

Rewrite the expression.

$\frac{2 a - 4}{3 a + 9} \cdot \frac{7 a + 21}{22 a - 44}$

Step 3

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

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Step 3.1

Factor $2$ out of $2 a$ .

$\frac{2 (a) - 4}{3 a + 9} \cdot \frac{7 a + 21}{22 a - 44}$

Step 3.2

Factor $2$ out of $- 4$ .

$\frac{2 a + 2 \cdot - 2}{3 a + 9} \cdot \frac{7 a + 21}{22 a - 44}$

Step 3.3

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

$\frac{2 (a - 2)}{3 a + 9} \cdot \frac{7 a + 21}{22 a - 44}$

Step 4

Factor $3$ out of $3 a + 9$ .

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Step 4.1

Factor $3$ out of $3 a$ .

$\frac{2 (a - 2)}{3 (a) + 9} \cdot \frac{7 a + 21}{22 a - 44}$

Step 4.2

Factor $3$ out of $9$ .

$\frac{2 (a - 2)}{3 a + 3 \cdot 3} \cdot \frac{7 a + 21}{22 a - 44}$

Step 4.3

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

$\frac{2 (a - 2)}{3 (a + 3)} \cdot \frac{7 a + 21}{22 a - 44}$

Step 5

Factor $7$ out of $7 a + 21$ .

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Step 5.1

Factor $7$ out of $7 a$ .

$\frac{2 (a - 2)}{3 (a + 3)} \cdot \frac{7 (a) + 21}{22 a - 44}$

Step 5.2

Factor $7$ out of $21$ .

$\frac{2 (a - 2)}{3 (a + 3)} \cdot \frac{7 a + 7 \cdot 3}{22 a - 44}$

Step 5.3

Factor $7$ out of $7 a + 7 \cdot 3$ .

$\frac{2 (a - 2)}{3 (a + 3)} \cdot \frac{7 (a + 3)}{22 a - 44}$

Step 6

Factor $22$ out of $22 a - 44$ .

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Step 6.1

Factor $22$ out of $22 a$ .

$\frac{2 (a - 2)}{3 (a + 3)} \cdot \frac{7 (a + 3)}{22 (a) - 44}$

Step 6.2

Factor $22$ out of $- 44$ .

$\frac{2 (a - 2)}{3 (a + 3)} \cdot \frac{7 (a + 3)}{22 a + 22 \cdot - 2}$

Step 6.3

Factor $22$ out of $22 a + 22 \cdot - 2$ .

$\frac{2 (a - 2)}{3 (a + 3)} \cdot \frac{7 (a + 3)}{22 (a - 2)}$

Step 7

Cancel the common factor of $2 (a - 2)$ .

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Step 7.1

Factor $2 (a - 2)$ out of $22 (a - 2)$ .

$\frac{2 (a - 2)}{3 (a + 3)} \cdot \frac{7 (a + 3)}{2 (a - 2) (11)}$

Step 7.2

Cancel the common factor.

$\frac{2 (a - 2)}{3 (a + 3)} \cdot \frac{7 (a + 3)}{2 (a - 2) \cdot 11}$

Step 7.3

Rewrite the expression.

$\frac{1}{3 (a + 3)} \cdot \frac{7 (a + 3)}{11}$

Step 8

Cancel the common factor of $a + 3$ .

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Step 8.1

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

$\frac{1}{(a + 3) \cdot 3} \cdot \frac{7 (a + 3)}{11}$

Step 8.2

Factor $a + 3$ out of $7 (a + 3)$ .

$\frac{1}{(a + 3) \cdot 3} \cdot \frac{(a + 3) \cdot 7}{11}$

Step 8.3

Cancel the common factor.

$\frac{1}{(a + 3) \cdot 3} \cdot \frac{(a + 3) \cdot 7}{11}$

Step 8.4

Rewrite the expression.

$\frac{1}{3} \cdot \frac{7}{11}$

Step 9

Multiply $\frac{1}{3}$ by $\frac{7}{11}$ .

$\frac{7}{3 \cdot 11}$

Step 10

Multiply $3$ by $11$ .

$\frac{7}{33}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{33}$

Decimal Form:

$0.\overline{21}$