Basic Math Examples

$\frac{2 w - 12}{49} \div \frac{w - 6}{14}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{2 w - 12}{49} \cdot \frac{14}{w - 6}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $7$ .

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Step 2.1.1

Factor $7$ out of $49$ .

$\frac{2 w - 12}{7 (7)} \cdot \frac{14}{w - 6}$

Step 2.1.2

Factor $7$ out of $14$ .

$\frac{2 w - 12}{7 \cdot 7} \cdot \frac{7 \cdot 2}{w - 6}$

Step 2.1.3

Cancel the common factor.

$\frac{2 w - 12}{7 \cdot 7} \cdot \frac{7 \cdot 2}{w - 6}$

Step 2.1.4

Rewrite the expression.

$\frac{2 w - 12}{7} \cdot \frac{2}{w - 6}$

Step 2.2

Multiply $\frac{2 w - 12}{7}$ by $\frac{2}{w - 6}$ .

$\frac{(2 w - 12) \cdot 2}{7 (w - 6)}$

Step 3

Simplify the numerator.

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Step 3.1

Factor $2$ out of $2 w - 12$ .

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Step 3.1.1

Factor $2$ out of $2 w$ .

$\frac{(2 (w) - 12) \cdot 2}{7 (w - 6)}$

Step 3.1.2

Factor $2$ out of $- 12$ .

$\frac{(2 w + 2 \cdot - 6) \cdot 2}{7 (w - 6)}$

Step 3.1.3

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

$\frac{2 (w - 6) \cdot 2}{7 (w - 6)}$

Step 3.2

Multiply $2$ by $2$ .

$\frac{4 (w - 6)}{7 (w - 6)}$

Step 4

Cancel the common factor of $w - 6$ .

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Step 4.1

Cancel the common factor.

$\frac{4 (w - 6)}{7 (w - 6)}$

Step 4.2

Rewrite the expression.

$\frac{4}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{7}$

Decimal Form:

$0.\overline{571428}$