Pre-Algebra Examples

$\frac{5 x - 5}{27} \div \frac{9 x - 9}{18}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 x - 5}{27} \cdot \frac{18}{9 x - 9}$

Step 2

Cancel the common factor of $9$ .

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Step 2.1

Factor $9$ out of $27$ .

$\frac{5 x - 5}{9 (3)} \cdot \frac{18}{9 x - 9}$

Step 2.2

Factor $9$ out of $18$ .

$\frac{5 x - 5}{9 \cdot 3} \cdot \frac{9 \cdot 2}{9 x - 9}$

Step 2.3

Cancel the common factor.

$\frac{5 x - 5}{9 \cdot 3} \cdot \frac{9 \cdot 2}{9 x - 9}$

Step 2.4

Rewrite the expression.

$\frac{5 x - 5}{3} \cdot \frac{2}{9 x - 9}$

Step 3

Multiply $\frac{5 x - 5}{3}$ by $\frac{2}{9 x - 9}$ .

$\frac{(5 x - 5) \cdot 2}{3 (9 x - 9)}$

Step 4

Simplify the numerator.

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Step 4.1

Factor $5$ out of $5 x - 5$ .

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Step 4.1.1

Factor $5$ out of $5 x$ .

$\frac{(5 (x) - 5) \cdot 2}{3 (9 x - 9)}$

Step 4.1.2

Factor $5$ out of $- 5$ .

$\frac{(5 (x) + 5 (- 1)) \cdot 2}{3 (9 x - 9)}$

Step 4.1.3

Factor $5$ out of $5 (x) + 5 (- 1)$ .

$\frac{5 (x - 1) \cdot 2}{3 (9 x - 9)}$

Step 4.2

Multiply $2$ by $5$ .

$\frac{10 (x - 1)}{3 (9 x - 9)}$

Step 5

Simplify the denominator.

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Step 5.1

Factor $9$ out of $9 x - 9$ .

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Step 5.1.1

Factor $9$ out of $9 x$ .

$\frac{10 (x - 1)}{3 (9 (x) - 9)}$

Step 5.1.2

Factor $9$ out of $- 9$ .

$\frac{10 (x - 1)}{3 (9 (x) + 9 (- 1))}$

Step 5.1.3

Factor $9$ out of $9 (x) + 9 (- 1)$ .

$\frac{10 (x - 1)}{3 (9 (x - 1))}$

$\frac{10 (x - 1)}{3 \cdot 9 (x - 1)}$

Step 5.2

Multiply $3$ by $9$ .

$\frac{10 (x - 1)}{27 (x - 1)}$

Step 6

Cancel the common factor of $x - 1$ .

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Step 6.1

Cancel the common factor.

$\frac{10 (x - 1)}{27 (x - 1)}$

Step 6.2

Rewrite the expression.

$\frac{10}{27}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{10}{27}$

Decimal Form:

$0.\overline{370}$